In this version of Mozart's German Dances, the third section of each dance has "Trio." engraved above the staff. What does this indicate?
It usually means it is the Trio section from a Minuet and Trio form. And, although the beginning of the score you link to is not marked "Minuet", it is in 3/4 and in the style of a Minuet.
Originally the Minuet was a kind of dance, with Minuet also describing the associated 3/4 dance music form. Later it became common to combine this form with a Trio section, creating a longer structure.
When this form first became common the Trio section would be literally that, a section scored for only three instruments, but the term continues to be used even where the instrumentation is for larger forces. However, even where the ensemble is larger, the Trio section usually has lighter orchestration and a simpler texture. This has particular relevance when one considers that the Minuet and Trio form was often used for the third movement of the classical four-movement symphony.