Awww man the opportunity to educate a newbie on RPGs. I love it!!!
Okay in D&D you have dice. These games use those same dice.
You have 4-sided dice, 6-sided dice (these are the dice most people know), 8-sided dice, 12, and the ALL IMPORTANT 20 sided dice.
In the game, the "dice" is abbreviated. So a 20 sided die is called a d20. A six-sided die is a d6, and so on.
In D&D the 20-sided die is used for your to-hit rolls. So when you turn on logging in Icewind Dale or Baldur's gate, and you see your "to hit" rolls, you want to see 20's there. Your character "rolls" a 20 sided die. Whatever he rolls is compared to his THAC0 modified by the enemy's AC.
So if your THAC0 is a 10, and the opponent has an AC of 3, you need to roll a 7 or better on your 20-sided die to hit him.
Now most weapons and spells use dice besides the 20. The damage for most weapons is listed as the number of dice, the type of dice, and then the modifier. So when a weapon has damage of "1d6+1" they mean you roll one six-sided die, and then add 1 to the result. You might get a strength bonus on top of that roll when you actually hit with it, but that 1d6+1 is the basic dice you roll.
Spells work similarly. A Fireball spell does D6 damage for every spellcaster level you have. So for example an 8th level Wizard who casts fireball will deal 8d6 damage. That's eight six-sided dice rolled and added together. If you fail your saving throw versus the spell, you take ALL that damage. If you pass the saving throw, for most spells that means you take half.
Magic Missile for example is one missile for every two wizard levels you have. So a 7th level wizard gets 1 missile at level 1, two missiles at level 3, three at 5, and 4 missiles at level 7. Each individual missile does 1d4+1 damage. You'd roll that 4 times.
Healing is also similar, and usually done in D8. A basic "Cure Light Wounds" spell will heal a D8 for every Cleric level. So a 5th level Cleric will heal 5D8 with a Cure Light Wounds spell.
Does that help?