Proficiency is a system that measures a character's aptitude with a particular skill. Each character's skill can be ranked from untrained to legendary, and each rank above untrained provides a bonus to checks. The proficiency scale for skills is as follows:
Untrained (-2): You have no idea what you're doing.
Apprentice (+0): You know the extreme basics.
Trained (+2): You are a competent professional.
Advanced (+4): You are highly experienced.
Expert (+6): You are among the best in your city.
Master (+8): You are among the best in the world.
Legendary (+10): You are historically, almost supernaturally proficient.
Sometimes, succeeding at a particular task requires a character to have a specific proficiency rank in addition to a success at the check. Locks and traps often require a certain proficiency rank to successfully use the Pick a Lock or Disable a Device actions of Larceny. A character whose proficiency rank is lower than what's listed can attempt the check, but they can't succeed. You can apply similar minimum proficiencies to other tasks. You might decide, for example, that an electronic trap that uses a console requires training in Computers to understand. An untrained soldier who struggles with Word Processors can't succeed at the check, but she can attempt it if she wants!
Sometimes you need to quickly set a difficulty class. The easiest method is to select a simple DC from the Simple DCs table by estimating which proficiency rank best matches the task (that rank is usually not required to succeed). If it's something pretty much anyone would have a decent chance at, use the untrained DC. If it would require a degree of training, use the DC listed for apprentice trained, advanced, expert, master, or legendary proficiency, as appropriate to the complexity of the task. For example, say a PC was trying to uncover the facts behind a conspiracy theory. You determine this requires a check to Recall Knowledge, and that only someone with master proficiency in Occult Lore would know the information, so you'd set the DC at 30—the simple master DC.
Untrained: DC 5
Apprentice: DC 10
Trained: DC 15
Advanced: DC 20
Expert: DC 25
Master: DC 30
Legendary: DC 35