Why is it important that the blocks are cryptographically linked together?
The idea builds on a security property of cryptographic hashes, that they are designed to be hard to invert (so-called one-way or pre-image resistant property).
You can compute y from x cheaply y=H(x) but it’s very hard to find x given only y. A full hash inversion has a known computationally infeasible brute-force running time, being O(2^k) where k is the hash size eg SHA256, k=256, and if a pre-image was found anyone could very efficiently verify it by computing one hash, so there is a huge asymmetry in full pre-image mining (computationally infeasible) vs verification (a single hash invocation).
What does the block structure look like in bitcoin?
Bitcoin mining uses the hashcash proof of work function; the hashcash algorithm requires the following parameters: a service string, a nonce, and a counter. In bitcoin the service string is encoded in the block header data structure, and includes a version field, the hash of the previous block, the root hash of the merkle tree of all transactions in the block, the current time, and the difficulty.