Why does gaining a hydrogen in biology considered reducing a molecule?
Hydrogen can accept electrons or donate them, so it can get a bit confusing. For instance, hydrogen donates electrons from a reducing agent. For example, in biology, consider cellular respiration. A co-factor will carry electrons often by reducing an atom with a nitrogen.

Consider NADP+ to NADPH. 



The nitrogen atom on the Pyridine group has an oxidation state of +1. When it picks up a hydrogen, to become NADPH, the oxidation state will go to 0 by gaining electrons brought by the hydrogen. Although the hydrogen doesn't bond to the nitrogen directly, it breaks the double bond on the para carbon (The carbon on which the new hydrogen is attached) at the top of the ring, and thus distributes the electrons to the nitrogen.

EDIT -
Hydrogen comes from some reducing agent, not a free hydride I'm sure.