Cryptography Fundamentals
Cryptography is the science of protecting information so that only intended parties can read or verify it.
In depth
In crypto, cryptography is used less for secrecy and more for proof: proving you own an address, proving a message has not been altered, proving a block was expensive to produce. Its security rests on maths problems that are trivial in one direction and practically impossible in reverse. That one-way property underpins hashes, keys and signatures.
Why it matters
The "crypto" in cryptocurrency is this — without it there is no ownership and no security.