Kovri will be used for Monero wallets and nodes, but how else will Kovri benefit Monero in the future? I thought I heard Kovri could be used to safely access remote nodes for things like MiniNero in the future for mobile devices, is this true?
Kovri will function as a full i2p router, thus increasing the utility of the i2p network overall, and providing the Monero user a gateway into that network. i2p is The Private Internet - its really its own network, you can sort of think of it like America Online back in the day. If you didn't use AOL in the early 90's, it was not the internet. AOL had its own subnetwork, almost, and if you wanted to browse the internet (not that there was much to browse in the early 90s), well then you had to essentially leave AOL's cordoned-off area.
So, if there is a distinctly private internet, and there is a distinctly private internet-currency, Kovri will essentially create the Monero-centric world.
And yeah, you can also access remote nodes. Actually, you can do that now already using an independent i2p router.