Blockchain technology is the foundation for cryptocurrencies, but it can also be used in a wide variety of other situations as well. What it is, in essence, is a ledger that is connected by thousands of computers. This makes it safe because if you’re trying to hack the blockchain, you’re hacking into a large network. This is drastically different from, say, hacking into a computer at a bank. There’s only one computer you need to deal with to compromise the system. With blockchain, that’s impossible.
And again, that’s where your payments are recorded and processed.