Character classes are a funny thing - ideally, every class should contribute something useful to the party as a whole. For some of these, there's an obvious combat-related use. But in most RPGs, combat isn't the be-all, end-all of everything - there are times you're doing something that doesn't involve sticking sharp bits into squishy people. Thus, most RPGs have what are called "skills" or "non-weapon proficiences" or whatever else you prefer - ways of judging how good a given character is at something non-combat related.
The Skill Monkey is a common designation for classes whose primary focus is their proficiency at using skills. They are often ill-equipped for combat, or at least direct combat, but they contribute to the party by tackling those pesky little problems that rely on people actually knowing stuff other than hacking 'n' slashing or blowing shit up. Sub-specializations of Skill Monkey include the Face, who specializes in Charisma type skills and so is usually the guy/gal doing all the talking for the party, the Sage, who specializes in Intelligence and/or Wisdom related skills, and the Fingers (sometimes "Fingers McStealey"), who is usually called on to do the traditional thief things (dealing with traps and locks, picking pockets and other slight of hand).
Two of the most iconic Skill Monkey classes for Dungeons & Dragons are the Rogue and the Bard, who both receive large amounts of skill-points and have easy access to a diverse array of skills. Wizards also double as Skill Monkeys, to an extent; during the days of Advanced Dungeons & Dragons, many kits emphasized this trait, particularly in the "Sage" direction.