You don't need to know about TCP handshakes to use the Internet. You do need to be sold on the benefits of cryptocurrencies to start using one (other than that the price for them is going up).
This thread is about blockchains not crypto-currencies. The fact the two are conflated as frequently as they are is quite unfortunate.
A great use case is in EHR. Your doctor, your insurance company, and all their BAAs participate in private block chain that controls access to your records. Any time a record is accessed, the chain is updated.
That's actually a horrible use case, becayse, while it is essential that covered entities track and be accountable for access to a record, the details of that access itself leak information to which access should be minimized, but instead it unnecessarily leaks across organizational boundaries to people who have no legitimate need for it.
A great use case is in EHR. Your doctor, your insurance company, and all their BAAs participate in private block chain that controls access to your records. Any time a record is accessed, the chain is updated.