Blockchain

Blockchain is essentially a group maintained database. It is most frequently applied to cryptocurriencies because it allows the whole community to either validate or invalidate transaction histories. This is useful because if someone attempts to create a false transaction history that goes into the next block then it can be rejected because the majority of other people will detect that it is incorrect. By design it is very difficult to falsify and were it to be successfully and consistently broken then it would become worthless as it's value lies in people agreeing to hold value in it and if it becomes untrustworthy they would immediately stop using it in favor of another cryptocurriency.

Basically how it works is by hashing. Each "block" is a hash of hashed transactions plus the hash of the last block but in order to finish a block you have to solve a puzzle that can only be worked out by brute force. The puzzle is usually a leading 0 problem where they give you some number and they want you to add something to it and the result must hash to something with some leading number of 0's. The number of 0's required is scaled so that it will on average take some rough amount of time so that blocks actually have some content before they are added to the chain. Once someone solves the puzzle everyone can easily verify that it's correct and then they move onto trying to solve the next block.

A lot of companies are trying to use blockchain in places that really aren't suited for it but because it's a huge up and coming technology everyone wants to say that they're using it. It's use case is fairly limited in that it only really works well for problems where you require group consensus before changing something in the database. The benefit of using a blockchain in this situation is that you can be sure that it is very secure. The drawbacks would be things like you have to have a network of people using it and constantly working on solving blocks which can require high power gpu's working almost always which will add up in electricity costs.