The Vertical Slice milestone is complete when the team has fully created one level of the game. The purpose of a vertical slice is to give the designers a template for how to create additional levels. In creation of the vertical slice level the designers would find any problems with the way the game is supposed to work. Once these problems are resolved, the rest of the design team can begin the creation of other levels much more quickly.
Previous Milestone: http://videogamebuzzwords.wikia.com/wiki/Proof_of_Concept_Gameplay_(POCG)
Next Milestone: http://videogamebuzzwords.wikia.com/wiki/Alpha