On: Bank of America's Research Report on Bitcoin [pdf]

[salient]

You can use just one. Some like to play it safe, though, and keep an "active wallet", where they have a small portion of their money (especially if they have a lot of Bitcoins), and they keep the rest backed-up (and encrypted) and somewhere safe, locally, to protect themselves against hacks.

[k__ → salient]

Is the wallet just a local concept?

The understanding I got after reading those guides online is like this:

the addresses are public keys

the blockchain knows how much money every address owns

the wallet holds the public and privat keys

is this right?

[javert → k__]

Precisely.

Although a public keys can be re-created from the private key, so the wallet doesn't have to store that.

And the address is actually a hash of the public key, to make it shorter and more readable.