(This article explains the mechanics of what a skill is. For a list of skills with their uses, see that article.)
A skill is an action your character can perform, it's success is affected by how much you have train the correct skill and by your natural capacities (for example, having a high Dexterity makes you better at tumbling). As you increase in level you can spend points into skills in order to be more successful at it.
Skill points and Skill Ranks
Each level, skill points are spent to increase skill ranks, which improve your bonus when making skill checks with that skill.
Skills and Difficulty Class
When using a skill, your are most likely trying to defeat a score. For example, when an Artificer or Rogue is trying to disarm a trap, he must beat a certain score to disarm the trap, that score is the difficulty class.
When using active skills, you are always trying to beat a DC. Whether you are intimidating a foe or searching for a secret door. Most of the time, you will have to roll a dice, sometimes you won't. When a dice is rolled, a natural 1 or a natural 20 does not grant an automatic failure or success.
When using passive skills, you are not necessarily trying to beat a DC. For example, when jumping, simply your skill modifier is taken in account to determine height of your jumps. Most of the time, you won't have to roll a dice when using passive skills, sometimes you will. When a dice is rolled, a natural 1 or a natural 20 does not grant an automatic failure or success.
Source of miscellaneous modifiers
It has been suggested this section should be merged.