Understanding some basic stuff first

Basic stats
 Abilities , also frequently called statistics, or base stats: those are Strength (how hard you hit and how much you can lift), Dexterity (how quickly you can move), Constitution (how tough you are to hurt), Intelligence (how much stuff you can learn), Wisdom (how well you use your knowledge), and Charisma (how much people are prone to like you). Points are assigned to these statistics depending on how lucky your rolls were at character creation.

 Ability modifiers:  The "default" value of a stat is 10, and any points above or below it determine what we call the ability modifier. In a nutshell, you want your modifiers to be as high as possible. For convenience, the modifiers for all base stats are usually referred to using the first three letters of each word, and I'm going to type them in capitals. (STR = Strength modifier, DEX = Dexterity modifier, etc.) The modifiers are calculated from the stat values, as follows:

Positive: 10/11 = 0; 12/13 =1; 14/15 = 2; 16/17 =  3; 18 = 4

Negative: 9/8 = -1; 7/6 = -2; 5/4 = -3; 3 = -4 (But if you rolled 3 on a stat, I'm having you reroll, this is unplayable).

Alignment:
The two alignment axes are Law vs. Chaos and Good vs. Evil, with Neutral in the middle of each axis. Choose where your character stands. Some classes have alignment requirements.

Law vs. Chaos - Lawful characters respect lawful authority, observe laws and mores, and generally follow the rules (A typical Lawful character will wait for a green light before crossing, even if the road is straight and empty as far as the eye can see.) Lawful characters CAN commit crimes, if they are acting in accordance with an inner code or custom that they find more important than the active public laws.

Chaotic characters are more of a "rules are meant to be broken" disposition, don't care about laws, and would rather skip lines, bypass procedures, and take shortcuts without regard for the consequences. If they need to meet the king, they are more likely to rush into the throne room unannounced, rather than wait for an audience (as a lawful character would.)

Neutral characters may act one way or the other. They may believe rules are generally there for a reason, but aren't above breaking them if it suits them.

Good vs. Evil

Good characters care about things like helping those in need, being kind to people, and generally loving thy neighbor and not harming innocents.

Evil characters care about themselves and maybe a limited few they are close to, and to hell with everyone else. That is not to say an evil character will always be a sociopathic jerk.They may actually be very charming, likeable, even good friends. But they would have no moral scrupules walking over an innocent's corpse, if that is the easiest way to achieve what they want.

Characters who are Neutral on this axis can sometimes be moved to be noble, kind and compassionate, but they can also be selfish, corrupt and wicked at times.

Alignment shift: If a Neutral character (on either axis) consistently acts as if they were on one end of the axis, their alignment may shift. Same happens if any character repeatedly acts contrary to their alignment. If a character's alignment changes, there may be consequences (some classes particularly require certain alignment). The DM has the last word in such cases.

Skills
 Skills represent how well you can do things. At level one you're given a certain number of skill points to put in your chosen skills, and at each next level you'll get additional skill points to distribute. The levels you end up with in a particular skill are know as skill ranks. Every skill is related to a particular ability, so to calculate your total skill, add your relevant ability modifier, racial or class modifiers if you have any, the current ranks, and any temporary modifiers you may have (such as bonuses from magic items, etc.) and you have your skill score.

Skills are measured in ranks (reflecting the number of skill points "spent" on them).

Class skills are the skills usually associated with a class. The maximum ranks that can be assigned to a class skill are equal to the character level+3 (i.e. a lvl 4 character can have max 7 ranks in a class skill.)

Cross-class skills are skills not typically associated with the character's class. Max ranks in cross-class skill = (character level+3)/2, rounded down (that means if you are lvl 4, max ranks in a cross-class skill for you will be 3.)

To gain a rank in a class skill, you need to spend a skill point on it. (1 rank "costs" one skill point)

To gain a rank in a cross-class skill, you need to spend 2 skill points on it. (1 rank costs 2 skill points)

Trained vs. Untrained skills - some skills can be used even if you have put no points in them (untrained). Then your checks will be based just on your dice rolls plus relevant ability modifiers. Some skills can be used only if trained, meaning that to use that skill, you need to have ranks in it (even if it's just 1).

Checks, saves, and difficulty (DC)
tl;dr - every thing has a difficulty (DC) and you need to pass it to succeed. When you roll to see if you succeed in doing something, it's called a check. When you roll to see if you can successfully avoid something that someone is trying to do to you, it's called a save.

checks - Every time you attempt to do something, you make a d20 roll. This is known as a check. You roll a check, for example, every time you do an action that requires some particular skill. Add your total skill value to the roll. This is your skill check result.

DC - The action you are attempting to do has a quality known as difficulty, expressed as a number typically referred to as DC (difficulty check). To succeed in doing something, you need a check result higher than the DC.

saves - In most situations where someone is trying to do something (usually harmful - attack, spell, magic effect etc.) to you, you'll get a chance to make a roll to see if you can avoid the effect. This is known as a saving throw, or save. Just like checks, saves have a DC; you pass the DC, you successfully avoided the effect (partially or fully); your save result is lower than the DC - you fail the save and suffer the effect.

HD and HP
 hit dice  (HD) - the type of die which is thrown to determine a character's  hit points (HP). At lvl 1, take the maximum possible result from the HD associated with your class, and add your CON. The result is your starting hit points (health). Every time you gain a level, you roll your HD and add the result to your HP.

Proficiency
Proficiency with weapons/armor means whether or not your character is skilled with the use of particular weapon or armor types. It is possible to use a weapon of wear armor you are not proficient with, but there will be penalties applied to your rolls.

Size, speed, and load
Size determines how much space you occupy on the combat grid (medium and small creatures take up a cell each, tiny can fit in a cell with another, large and huge can take up between 4-9 cells). Size also influences your lift/carry capacity. Although it is mostly calculated based on your Strength, some sizes additionally modify that capacity.

Speed is an indication of how fast your character can cover ground in combat. Each cell on the battle grid is considered to be 5ft in each direction. Your base land speed determines how many cells you can move across in a single turn. (example: speed 30 means you can move across 6 cells starting from the one next to you in the desired direction. Note: Just because you can cover 30 feet, it doesn't matter you must move 30 feet at every turn. Maybe you just want to move 5 ft - one cell - to the left.)

Load is how much weight is on you. That includes armor, weapons, plus anything you have in your backpack. Each character has a load capacity (again based on Strength); if that is exceeded, your base speed is reduced.

Random combat terminology
 range vs. reach:  Range is how far you can hit with a ranged weapon. Reach is how far you can hit with a long melee weapon (pike, halberd, longspear etc.) A longsword is not a reach weapon.

 AC and attack:  Armor class (AC) is an indication how difficult is for an opponent to hit you. It's based on your current armor, DEX and various other modifiers as applicable. Attack is how well you strike. It depends on your class, STR or DEX, and whatever miscellaneous modifiers you have. If an attack roll is higher than the target's AC, the strike hits and you can start calculating damage. Otherwise, the strike fails (misses).

 flat footed - Under certain circumstances (a character is surprised, has his back turned, is flanked, etc.), a target may lose the DEX bonus to AC.