If you've bought some bitcoin or are about to, chances are you'll go to an online agent such as coinbase. You'll exchange $€£ for example and receive some bitcoin. The coins will be placed in your new wallet held by coinbase.
2 types of wallet:
The first is an online wallet such as offered by coinbase. Understand that coinbase is one of many exchanges and you can potentially have multiple wallets held at multiple exchanges.
Your wallet with coinbase has an address just like a bank account number. As long as the company exists and its Web server is running you can have access to your coins.
The second type of wallet is a local one. This wallet is stored on one of your personal devices such as a laptop or smart phone. Again you can have multiple personal wallets on multiple devices. Each being unique.
Electrum offers downloadable software to set up your personal wallet. There are also a lot of wallet apps available for smartphones
Having a personal wallet means full control over your coins. However It also means full responsibility. If your pc crashes or your phone goes for a swim and you haven't created a back up. Bye bye coins!!!
I hope this aids in your understanding.