Can anyone please define what exactly the APT cache is?
apt-cache is a command to manipulate and obtain information from the packages at apt's cache.
It creates a repository of information about the packages that are avaiable from your sources list, so this way you can search packages and information about it.
Let's say you want to install a chat program but you don't know the name of a package for it.
You would open a console and type:
sudo apt-cache search chat
This would return a list of packages available and that refer to the word chat.
Typical operations with
Adds a package file to the source cache.
Builds both the package and source cache
Show some general information for a single package
Show some basic statistics
Show the entire file in a terse form
Print an available file to stdout
Show unmet dependencies
Check the cache a bit
Search the package list for a regex pattern
Show a readable record for the package
Show raw dependency information for a package
List the names of all packages
Generate package graphs for GraphVis
Don't forget to add package name after the commands listed above.