CW1 is a specification for proxy contracts based on CosmWasm. It is a very simple, but flexible interface designed for the case where one contract is meant to hold assets (or rights) on behalf of other contracts.
The simplest example is a contract that will accept messages from the creator and resend them from it's address. Simply by making this transferable, you can then begin to transfer non-transferable assets (eg. staked tokens, voting power, etc).
You can imagine more complex examples, such as a "1 of N" multisig, or conditional approval, where "sub-accounts" have the right to spend a limited amount of funds from this account, with a "admin account" retaining full control.
The common denominator is that they allow you to immediately
execute arbitrary CosmosMsg in the same transaction.
Execute{msgs} - This accepts Vec<CosmosMsg> and checks permissions
before re-dispatching all those messages from the contract address.
CanExecute{sender, msg} - This accepts one CosmosMsg and checks permissions,
returning true or false based on the permissions. If CanExecute returns true
then a call to Execute from that sender, with the same message,
before any further state changes, should also succeed. This can be used
to dynamically provide some client info on a generic cw1 contract without
knowing the extension details. (eg. detect if they can send coins or stake)