In most role-playing games, skills are abilities that represent the training or knowledge your character has gained throughout his or her life and career. In most systems, there is an explicit list of skills a character can take, representing actions that the designers thought were important or common in to play.
In a stat-based system, skills often provide a bonus to the attribute that "governs" the skill. In these systems, the skill acts as bonus to the base given by the governing stat. For example, having points in the Climb skill will improve your chances of succeeding at a Strength check to climb a surface.
When a game system calls a skill a "proficiency," it means the skill's purpose isn't to give a bonus to attempting an action, but cancels out a penalty that anyone else would have when making an attempt.
Certain games use a "cascade" system, where skills can be used as poor-quality replacements for other skills, or some skills are prerequisites for others. The "Pilot" skill in a sci-fi setting can cascade to "shuttlecraft," "fighters," "frigates," capital ships," etc. GURPS is the most (in)famous of these systems, where it's normal to consult flowcharts.