When a PC (Player Character) attempts an action - such as jumping on a table, throwing a punch, driving a car, casting a spell, etc - that might have consequences if it failed and isn't so easy it goes without saying that the PC will succeed (such as scratching one's nose or eating cereals), then a die roll is required. Said die roll is usually one of the following two:
D10 + Attribute + Skill (Or another Attribute) (Ex: Strength + Sports roll, or Dexterity + Constitution roll)
In the aforementioned example, a character with, say, Str 3, Dex 4, Con 2, Will 4, and a Sports skill of 2, would roll:
-1d10 + 8 (For the Willpower doubled roll) -1d10 + 5 (For the Strength + Sports roll) -or 1d10 +6 (For the Dexterity + Constitution roll).
Simply put, the GM will ask for a roll, the player rolls a D10 and adds the appropriate Attribute(s) and Skill, or doubled Attribute, or possibly two attributes, though less often so.
An action usually fails if the roll ends up a 8 or less, and it succeeds with a 9 or higher... though sometimes it depends. (Read below)
NOTE: Exceptions exist. Sometimes, a given event require an Attribute only roll (not doubled). In that case, the character only gets to add the given Attribute, once, to the roll. Sometimes it could be something else entirely. It depends.
Sometimes, succeeding isn't enough. Sometimes it matters most 'how well' one succeeds. For example, performing a long jump can be done fairly easily... but will it be long enough to reach the other end of that chasm? Or... sure, you punched the guy. But did you just barely slapped his cheek, or did you knock him out in one punch?
When such a situation arises, Success levels will have to be taken into account. Simply put, the greater the roll, the better one succeeds. The table below gives a good idea as to how it works:
Example time: Jack Black sings his latest hit, 'Master Exploder' to entertain a crowd in a bar. He has Dexterity 3 and Art 6, so even if he rolled a 1, he'd still get a total of 10, or 1 success. That's enough to play the song okay-ish. But he rolls a 10, for a total of 19, and soon enough the crowd goes completely nuts, chanting his name and rocking their heads to the music.
Sometimes, a given action will downright require a minimum level of success to succeed 'at all'. For example, maybe a bomb is very complex to disarm, and one has to obtain a Very Good result at the very least to successfully do so and avoid a very messy death.
Sometimes, an action's success may depend on another person's own actions. The most common example being, of course, combat. If you try to punch someone, they will very likely try not to get punched, unless they're Superman or something. If you open fire at someone with a gun, most people will normally try to be elsewhere than in the bullet's path. If you're playing poker with someone, or arm wrestling someone, said someone will likely try to win as well.
Those are 'Resisted Actions'. In that case, both people roll, and the best of them succeeds. Ties go to the defender if approriate. If both fail, no progress is made on either side and awkward silences ensue.
Example 1: Silent Bob (Dex 3, Kung Fu 3) has had enough of Jay's (Dex 3, Acrobatics 1) bullsh*t. He reaches back and moves to punch his best friend in the face. Bob rolls a 5, for a total of 11, and Jay tries to dodge with a roll of 3, total of 7. The latter fails, and get socked in the face.
Example 2: Hulk Hogan and "Macho Man" Randy Savage are arm-wrestling each other in the backstage. Both have Str 5, and make Str doubled rolls to win the arm-wrestling session. The two of them roll 6s, tying at 16. Since there is not really a defender here - both are equally trying to defeat the other - the GM simply rules they have to roll again.
So we know how basic actions work, that some actions must succeed to a certain degree to have any, or more, effect, and that some people may resist certain actions. Another important point is that sometimes, other, unrelated factors may also make things more easier, or more difficult, for the person trying to do something. Those external factors may modify a roll in positive, or negative, ways, and are usually completely under the GM's control.
Example 1: Eric is trying to drive home as fast as he can to help his brother out. Normally, it'd be a simple Dexterity + Driving action. However, there's a lot of traffic (the GM decides to apply a -2 here), and it's raining HARD (another -2). Eric has Dex 2 and Driving 1, so if he wants to get home as fast as he wants, it's probably going to end badly since he rolls with a total of -1 right off the bat.
Example 2: Helen wishes to program an awesome videogame, but she's on a cheap computer (-1), is really trying to make the gameplay complex and realistic (-2), and is on a stressful release time limit (-2). Luckily, she's a genius with Intelligence 6 and Computers 7, so she still rolls with a +8, meaning it'll probably be a great game nonetheless.
Nothing is impossible, it just hasn't been done yet.