When you need to validate a transaction is in a block
All of this info is relevant to the operation of a light-wallet, which does not fully validate the blockchain, but instead validates the longest chain of block headers, and any transactions that are relevant to that light-wallet.


  In what situation you want to validate a transaction is in a block.


Simply: to ensure that a payment you have sent, received, or are otherwise interested in has been included in the Blockchain record. If someone pays you a huge sum of Bitcoin, you'll probably want to be sure that payment was actually legit!


  How you find the block that the transaction could be in.


The text you quoted from Mastering Bitcoin has the answer: a full-node peer will use your bloom filter to provide you with transaction info relevant to your wallet.


  The relevance that specific block has to you. Even if you verify it's part of some block, I don't see why you care it's from that block.


In order to verify the transaction is included, you will need to know which block it is in. This will allow your wallet to calculate the cryptographic proofs (using the merkle root that is in the header) that let it verify a transaction has occurred on the network in a trust-minimized way. 

There is no way to similarly know that a transaction is included in the blockchain record, without knowing the specific block you need to check the cryptographic proofs against.


  So you prove that it's recorded in the blockchain. I don't see how this means it's valid.


Only valid transactions can be recorded in the blockchain history, though as a light-wallet, you are trusting that the network of full nodes is otherwise validating all blocks and transactions, to ensure no invalid data is included in the chain. As long as the full nodes are doing their job, invalid transactions cannot be included in the chain. Any miner that attempts to include an invalid transaction in a block, will see that block dropped by the network's nodes for being invalid.