A Wallet, whether it is a Software Wallet or a Hardware Wallet, manages your cryptocurrencies and makes them manageable to you.
The name Wallet is actually not that great. The name suggests that the coins or tokens you hold are actually inside the wallet, just like notes or coins would be. However, this paints a distorted picture.
A Wallet makes it clear which coins in the public ledger (the blockchain) you own.
In short, a Wallet manages your private key. This Private Key is made readable to people in the form of the Seedphrase and usually consists of 12 to 24 words that you need to store in a safe way and in the correct order.
A Hardware Wallet is safer than a Software Wallet because you can keep it offline under lock and key.