Concept

A skill challenge is a ruleset to formalise a party's objectives outside of combat. This might involve interrogation, tracking, getting into a locked dungeon, making sense of clues gathered or other things you wish to accomplish outside of combat. 
It works as following:
The DM explains the current predicament, either forced upon the players by one of their actions or happenstance, or chosen to be engaged with by the players
The players take turns picking one of their skills or abilities and explain in the narrative what they do an how this helps
They roll with the relevant skill against a DC. This DC is dependant on the challenge and on how well the skill fits it. There usually is predetermined list of skills that are easier
The party needs 2xPC wins before 1xPC fails
Criticals count for two
Repeat successful skills are more difficult 
Repeat failed skills are easier