Why does the blockchain need blocks? I think I understand the main parts of the Bitcoin blockchain. While I was explaining the concept to my girlfriend she asked me why groups of transactions are actually stored in a block? Every transaction is verified by every node, so why do we need blocks?

I had no answer to her question, so maybe a greater mind than me can explain why the blockchain needs the transactions to be stored in blocks?
A block is just an arbitrary grouping of transactions.  It makes a convenient chunk of data for a proof-of-work to be performed on.  You could hypothetically do the proof-of-work on the transactions themselves, and then chain them one after the other.  This, however, would fail miserably.  Blocks must reference the previous block, so if you just go by single transactions instead of blocks, you'd have wait for the proof of work on each transaction.  It means that you could only have a single transaction on the network per target time for the proof-of-work algorithm.  It's a terrible solution in terms of scaling.  This would also create other problems, particularly having to do with a miner's incentives, and the censorship-resistant nature of the network.  Groups of transactions are better to work with.