1. What is a wallet?
A wallet is a program (or way) to manage your Bitcoin addresses, e.g. keeping track of how many Bitcoins you have and allowing you to spend them.
I think first I have to explain how Bitcoin adresses work:
You have one public Bitcoin address to receive Bitcoins (e.g. 15ho8Uv3Ho42xMD7gF31pjNzjhmtnpA2wz )
And a corresponding private key to this address that allows you to spend them (in this case: 5HuwnVoEP8Uj3s15WohWjhJvVRBkeenhv39WjiHsDBcErPpaFav)
The private key is kinda like a password.
Everyone that knows this private key can access the Bitcoins.
2. If a wallet is a physical object (or part of one), what are examples of the most secure ones?
3. I have read that the safest way to store BTC is in an offline wallet, is this true? If so, how do you do this?
Yes, that's true.
If computer malware gets access to your private keys then those Bitcoins are gone, so it's better to keep the keys to bigger Bitcoin stacks offline.
The most secure ones are paper wallet and cold wallets.
A paper wallet is nothing more than the private key and public address printed on a piece of paper (and you are still able to receive Bitcoins, you only have to be online in order to spend them)
You can create those for example here:
https://www.bitaddress.orgCold wallets are the digital form of that, e.g. an wallet file on a usb stick, sd card, offline-laptop
(and there are also some more professional solutions like the Armory Offline wallet or Trezor)