Plain English Meaning
A TAA is a piece of airspace around an instrument approach that tells you the lowest safe altitude you can fly while heading toward the start of the approach, depending on the direction you're coming from.
Full Definition
A Terminal Arrival Area is a designated airspace associated with an RNAV (area navigation) instrument approach procedure that provides a transition from the en route structure to the approach. It is typically depicted on the approach chart as one or more sectors arranged around an initial approach fix, each with its own published minimum altitude. Pilots arriving within a TAA sector may descend to the charted and to the associated initial approach fix to begin the approach.