NB: I am seeking to understand how endorsements works in general. This will help me determine how to design applications when using Hyperledger Composer.
When I read
The endorsement policy enables you the chance to add an extra verification layer to your Blockchain. You define it when you create the channel.
So, you should define your Endorsement policy according to your requirements
The endorsement process is described in the docs. That said, in simple terms, the process of endorsement involves an endorsing peer signing the read/write set of a transaction proposal with its certificate. This basically says: the peer identified by the signing certificate asserts that these are the read/write sets of the proposed transaction simulation.
A client that invokes a proposed transaction will need knowledge of the endorsement policy for that channel/chaincode so that it can transmit the proposed transaction to each of the endorsing peers (or to a sufficient subset of endorsing peers to satisfy the policy). When it has received the responses from each endorsing peer, it will check that the transaction is valid and then broadcast the endorsed transaction to the ordering service, which will add it to a block and broadcast to the validating peers for that channel.
Validating peers will then validate the endorsement policy of the channel/chaincode against the transactions in a block to ensure that:
If the endorsement policy is satisfied, then the transaction is committed and the world state updated with the read/write set.
At present, Composer cannot manage the endorsement policy, but this is definitely on the development roadmap.