Assuming they're a new user, they may have had to switch browsers, install MetaMask, fund a wallet, switch networks, accept a connection request and sign a message. Phew. With all that considered it's probably best to let them know it's over and they're connected.
Nothing beats a friendly hello. This might be a cause for something like a toast message which pops up on connection and then gets out the way soon after, so they can start using your dapp.
Summarise their connected account
This is more of a permanent indication that they're connected. Now that they're connected your dapp can read their Ethereum address and balance. This is good information to provide your user so they can get this info at a glance without having to go into their wallet's UI. This information can also help them validate that it's the account they want connected.
So they're connected and they know it. But what if now that you've read their account balance you realise that they're not going to be able to use your blockchain features? You've got to help them get enough funds for transaction fees.