Initializer can send a transaction to the escrow program to initialize the Vault. In this transaction, two new accounts: Vault Authority's ATA and Escrow State, will be created and tokens (Token A) to be exchanged will be transferred from Initializer to Vault(short for vault authority's ATA).
Initializer can also send a transaction to the escrow program to cancel the demand of escrow. The tokens will be transferred back to the Initializer and both Vault and Escrow State will be closed in this case.
Taker can send a transaction to the escrow to exchange Token B for Token A. First, tokens (Token B) will be transferred from Taker to Initializer. Afterward, the tokens (Token A) kept in the Vault will be transferred to Taker. Finally, both Vault and Escrow State will be closed.