Computers these days are very fast and can calculate hundreds of thousands of hashes per second. You could effectively tamper with a block and recalculate all the hashes of other blocks to make your block chain valid again. So to mitigate this, blockades have something that is called proof of work. It's a mechanism that slows down the creation of new blocks in Bitcoin's case. It takes about 10 minutes to calculate the required proof of work and add a new block to the chain.
This mechanism makes it very hard to tamper with the blocks, because if you tamper with one block, you'll need to recalculate the proof of work for all the following blocks. So the security of a block chain comes from its creative use of hashing. And the proof of work mechanism. But there is one more way that block chain secure themselves. And that is by being distributed instead of using a central entity to manage chain block chains. Use a peer-to-peer network. And everyone is allowed to join.
When someone joins this network, he gets a full copy of the block chain. The node can use this to verify that everything is still in order. Now let's see what happens when someone creates a new block. That block is sent to everyone on the network. Each node then verifies the block to make sure that it hasn't been tampered with. And if everything checks out, each node adds this block to their own block chain. All the nodes in this network create consensus. They agree about what blocks are valid and which aren't. Blocks they're tampered with will be rejected by other nodes in the network.