For "why would I want to use this over a SQL alternative" see [2].
For "what kind of applications can I build with this?" see [1][2][3][4].
Cheers!
[1] https://www.bigchaindb.com/usecases/
[2] https://blog.bigchaindb.com/three-blockchain-benefits-ae3a2a...
[3] https://blog.bigchaindb.com/six-blockchain-application-verti...
[4] https://blog.bigchaindb.com/where-does-blockchain-scalabilit...