Adding a concrete example to Swashbuckler's correct answer:
When we talk of encryption, we talk of encrypting content with a key, not a password. Passwords are a specific kind of key, one that a user can reasonably type on a keyboard. I draw the distinction because, in encryption schemes with recovery keys, the data is indeed encrypted with a key, but that key is not your password.
They could indeed have used your password as a key. Let's say your password is password1 (a horrible password: never use anything like it). They could absolutely encrypt the harddrive using password1 as the key. However, let's say you forgot that password. There's nothing they can do to help, because that's the only key that decrypts the files. Or let's say you want to change the password. Now we have to re-encrypt every single file with a new key.
Systems like this solve both problems with a single solution. Instead of using your password as a key, they pick one for you. They pick some obnoxious binary string, typically 128 or 256 bits long, but for visual imagery, lets assume they pick an ASCII string like FAy."fts~j\bF7,h[WGT@y2W=erXq7P`. I told you it would be obnoxious. They encrypt your data with that key.
Now this key is great. You're never going to have to replace it because nobody is going to guess it in a million years. However, you wont be able to memorize it either! So if we don't do something more, your data will be useless!
These systems create another data file somewhere, where they encrypt the key, FAy."fts~j\bF7,h[WGT@y2W=erXq7P. They encrypt it using your password, password1, as a key. Now if you want access to your files, you provide password1`, they decrypt this little file, to get access to the ugly key, and then use that ugly key to actually decrypt things.
A recovery file is yet another data file somewhere, which also stores the ugly key, encrypted. It is encrypted with a different key. The form of the key depends on the individual product, but it might be something like 0138b300-7cf9-4eb9-b79d-f84a65e0ad68-313ed151-5ab0-47e6-867d-bf62f77953d6. It's the same game as before. If you have that password, you can use it to decrypt the ugly FAy."fts~j\bF7,h[WGT@y2W=erXq7P` key, and decrypt everything else.
The idea behind systems like these is that you end up creating two different passwords which can access the data, but which have very different use cases. While you may need to be able to memorize the first password so that you can type it every day, you may not mind storing a copy of the recovery key somewhere safe, and having to physically haul it out if you forget your first password.
Or, in the case of corporations, often the recovery key is entrusted to an IT team and corporate policies are used to ensure those individuals don't abuse the key, and corporate security ensures that no adversary gets their hands on them. In either case the pattern is the same: two passwords, but the way they are handled may be very different.
Obviously, if you forget both passwords (your real password and the recovery one), you're stuck. Typically this means you store the recovery one somewhere that you can rely on. Safety deposit boxes in banks might be a good place for some (always figure out a threat model, then decide where it is safe to store these passwords).
Another fancy trick that can be done is to use an algorithm to generate the recovery password. This can let you do clever things like break a password into 3 parts, give one to a CEO, one to the head of IT, and one to the chairman of the board. No one of them can use the key on their own, but put the three parts together, and you can generate the key.
