Bonuses and penalties apply to checks and certain statistics. There are several types of bonuses and penalties. If you have more than one bonus of the same type, you use only the highest bonus. Likewise, you use only the worst penalty of each type.
When a character attempts an action where success is uncertain, they may roll a check. This is a roll of one 20-sided die plus the named proficiency bonus. For example, a Perception check would add your Perception proficiency.