How do wallets store private keys?

[WiW]

New to forums. Yay!

So I'm looking at this Android app, and I can export the private keys to my bitcoin addresses, but I'm asked to enter a password to encrypt the exported keys... So the wallet won't actually show me my private key.

My understanding is that this private key (when unencrypted) should give me (or anyone writing it down for themselves) the access/ability to use the bitcoins in that address. Is this correct? And if so, which wallet will show me this private key in plaintext?