The bitcoin blockchain is a replicated database (not distributed, as this guy claims) which contains a copy of each and every bitcoin transaction ever made since the beginning of time. It's basically how they 'solve' the so-called double spending problem where a digital coin can be duplicated (spent twice) unless there is some way to verify the uniqueness of said coin. Given a total history of every transaction ever made, a recipient can check whether a coin hasn't been already given to someone else by the sender.
The idea is that anyone can participate in the peer-to-peer network that maintains this database, and that this database is signed on a block-by-block basis by the participants to maintain consensus. Hence the term 'block chain'.
Now, since the data in the block chain is a set of time-stamped transactions that are difficult to forge (unless someone controls >50% of the network), one can use it to store other time stamped information such as contracts.
(disclaimer: the above is just a semi-laymans attempt to explain the block chain to OP, feel free to correct me where I am wrong:)