Character level is the sum of the levels for each of a character's classes (with up to three classes allowed). This is the equivalent of hit dice for monsters, and in general it is a measure of the power of a character. New character levels are earned on the basis of experience points, but are not counted until the player completes a level-up.
When Neverwinter Nights was first released, player characters were limited to character level 20, the highest level supported by the core rulebooks for third edition Dungeons & Dragons. While level 20 is quite an achievement, installing Hordes of the Underdark allows epic levels, raising this limit to 40. (The Shadows of Undrentide expansion does not affect the level limit.)