The American security researcher Dan Kaminsky is quoted as "The first five times you think you understand [Bitcoin], you don’t". You will need some time to grasp those concepts (Bitcoin is basically an application that has the Blockchain as a building block) and just reading some definitions will not help you much. There is a free MOOC on Coursera entitled "Bitcoin and Cryptocurrency Technologies" from Princeton University, which I highly recommend.
As far as trust is concerned, you must be aware that Blockchain technology can also be used for supervision and to exert power. In this respect it might have many advantages and disadvantages, most of which are not fully explored yet.
Blockchain is a peer-to-peer network of computing nodes where any node on the network has to be validated before interacting with other nodes and where this interaction is never complete until a miner(s) (a node or group of nodes) executes the mining process. The mining process takes care of the cryptographic processes as well as other processes and synchronisations that ensure that the action or interaction or transaction initiated by a node is transparently completed (permanently) recorded as a block on the existing chain of previous blocks.