Cryptography is nothing but a Hard Maths Problem.
Public Key Cryptography or Asymmetric Cryptography is a concept which is being used almost everywhere nowadays. Prevalent uses could be considered on the internet where we need to have a trust factor within different parties.
Let's start with Asymmetric word first.
First thought which will come to your mind will be "Do we also have Symmetric?". Yes you are right. We have Symmetric Cryptography as well.
What is Symmetric Cryptography?
First and foremost thing is that in cryptographic world, we have a concept of keys. Just like we have keys and lock to make the home secure, similarly we have keys here to make the data secure.
We lock the data using one key A and then unlock it using key B.
In symmetric cryptography, both the keys are same (A==B). The main advantage of these kind of keys is that they are faster than their siblings.
In asymmetric cryptography, we have 2 different keys. We can use Public Key to encrypt the data and Private Key to decrypt it. Public Key is known to everyone. Private Key is only known by us.
So public key cryptography or asymmetric cryptography uses 2 keys separately for encryption and decryption of data. They are much more secure but they uses a lot more computation power to encrypt and decrypt.
Blockchains and HTTPS are some examples where we use the public Key Cryptography.