What does "smart wallet" mean?

In a smart wallet, each user account is actually a smart contract, rather than a simple cryptographic keypair. This allows many advanced features, such as:

• Batching multiple operations in one transaction - this actually enables one-click DeFi deposits and operations, and eliminates ERC-20 approvals from a user perspective. This also reduces gas costs.
• More sophisticated authentication and permissions - a single account may be controlled through different keys. For example you can login with email/password, then move to hardware wallet based authentication, without having to move funds manually. Or, you can use both, and have the email/password authentication be restricted to a certain daily limit.
• Gas abstractions - this means that you don't have to pay gas in ETH, but you can pay in any token you have, making transaction fees a way easier experience.

This approach has multiple advantages, and in fact account abstractions (another way of saying "smart wallet") have been discussed as being superior a long time ago, and Vitalik has made a recent effort to standardize them.

The main reason why very few wallets work this way is that:

1) They're more challenging to build;

2) Up until recently, smart wallets posed some additional limitations (e.g. signing messages before EIP 1217).

Our experience with building smart wallets goes way back to 2019, since since the Ambire AdEx Platform started using a form of a smart wallet internally to enable paying fees in DAI, batching multiple actions together, etc.