What is Cryptography?
Basically cryptography is the art of changing sensitive information into text called 'cipher text' (text that looks like it was created when someone's cat sat on a keyboard) which can only be decoded with a 'cipher key' (think of it as a master key that unlocks your protected information) . This allows you to protect your information as only you and people who have your 'cipher key' can successfully decode it. That being said there are people called 'cryptoanalysts' who specialize in breaking these codes without using the necessary keys (but seriously unless you're planning on selling government secrets or are part of a blockbuster spy film you're pretty safe from these guys).

Changing Plain Text to Cipher Text
An algorithm is 'a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer'. In cryptography, algorithms are used to turn plain text into cypher text by using a set of rules given by the user. To the right is an example of a basic algorithm where a positive integer is used as the input and is returned to a positive integer in the output.To change plain text into cypher text you can use one of two techniques, symmetric or asymmetric encryption.
Symmetric encryption is the earliest kind of encryption, primarily the process that I spoke of during the first paragraph. It has been used through the ages to stop secrets and sensitive documents being leaked to the wrong people (e.g. Henry VII, Justin Bieber, my creepy uncle Jeff).
The algorithm could use a rule as simple as shifting all characters in the alphabet up 2, for example all A's become C's, J's become L's and so on. In this example the cipher key would simply change the letters back to their original state. But as long as you make a cipher key you can get a little more creative, for example you could replace all H's with %, or all R's with 5's.
HTTPS
HTTPS is at it's core a very simple and useful process that is used by offices and huge company chains alike. HTTPS or the Hypertext Transfer Protocol System is used on secure servers to help keep information safe as it adds an extra layer of defense.Once a client (e.g. You) has connected to a sever

HTTPS is popular on the internet as it authenticates the website and it's server with which it is communicating to, this helps protect again certain kinds of 'web attacks' (bad things that want to steal your details). It also uses both encryption and decryption, encrypting the clients information when it is sent to the server and decrypting it when it reaches its destination. This allows protection from eavesdropping and tampering from third parties. When used together, all layers of protection that the HTTPS provides allows the user to ensure that the information that is being sent / received is between the correct people and that the information is safe from any third party.
Public Key Infrastructure
A public key infrastructure (or PKI) is defined as 'a hardware, software, people, policies, and procedures needed to create, manage, distribute, use, store, and revoke digital certificates and manage public-key encryption'. Basically it is used to properly protect data by only allowing authenticated users to access certain information. This is done by giving 'keys' (long alpha-numerical strings of code that acts like a digital key) to the user to allow them to access specific information. There are two main types of key, a 'private key' and a 'public key'. The 'private key' is owned by an individual, and all 'public keys' are created from this and distributed freely to whoever owns the 'private key'. These 'public keys' can then be classified into levels, allowing users with a higher level of key to access corresponding files with a higher level 'lock'.