How's your math?
Put simply (?!): a block chain (blockchain, all one word, is only the last couple of years) is a series of records (aka ordered set of data blocks) linked (aka cryptographically chained) via a method that:
* locks each data block disallowing alteration and/or removal;
* enables new blocks to be be successively (not retroactively) added;
* verifies the authenticity of each block, their order, and the completeness of the set.
Each block includes, besides it's particular data (which can actually be null):
* the hash or similar cryptographic identification of the prior block, and/or
* the key to decipher the subsequent block in the series.
Each block typically but not necessarily may include:
* timestamp of creation;
* digital signature of contents (aka payload).
The order/sequence of a particular blockchain is represented via a directed graph (a set of nodes, each pair of connected via directed edges (aka arrows). N1 ----> N2 ----> N3 ...
The idea goes back to the early 90s as a method of collecting (connecting) documents into one organised grouping (block). However, it was Satoshi Nakamoto's 2008 paper that really purposed the idea.
Basically, at it's most fundamental, a blockchain is a secure distributed database. It's greatest weakness is that it grows over time, as it can be reconstituted from any one point: Bitcoin took from 2009 to 2015 to grow to 30GB; however, it grew from 50GB to 100GB through 2016.
The potential usages are considerable, especially in finance, however there is currently no everyday practical breakout use besides cryptocurrencies, which, imo, are currently a hazardous investment/involvement for the general public.
Government likes the idea, broadly, because it allows (theoretically) every individual's interactions to be connected and recovered. However, most government conceptual ideas I've read include removing the distributed underpinning and replacing it with a central aka their database. The greatest weakness becomes erroneous data input, possibly in error, possibly in spite, that cannot be retroactively corrected.
I haven't had time to pay much attention to get much deeper an understanding beyond the above. I do see serious perhaps critical problems and possible attack vectors that are not part of the jump on the bandwagon conversation.