One use case is searching multiple gmail accounts.

I often need to search for a message in my secondary account (I'm logged into my primary acct in Safari on my iPhone). Before this, the options were:

1. Log out of primary account and log into secondary account (laborious, especially if you use 2-step auth) and search in the gmail webapp.

2. Search using the iPhone mail app (awful).

(Makes me miss Android's native gmail app.)

Greplin searches both email accounts and tons of other useful stuff.