Git is a version control system (VCS) which was originally developed by Linus Torvalds to use for developing the Linux kernel.
Suppose you're starting development on a big project. You decide that you to backup your code periodically in case you need to retrieve old code (for example if you changed something which introduced a bug, or if you accidentally deleted a section of code).
You could just set up a script to backup your project directory every day to another directory, or maybe an external drive. But then if you do lots of work in a day and then lose your data, you'd have no way to retrieve it. So you need to choose when to backup.
From now on, I'll call backups 'snapshots'. Now we have a system where
every time you want to create a snapshot, you make a copy of your entire
project directory into a new directory, say snapshot-X where X is the
snapshot number.
So that you can easily remember what you did in each snapshot, you add a
message file which contains a short summary of the changes you made.
And now we've come to the basics of a VCS. A new snapshot is created with each commit, and a message (along with a date and author) is attached to each commit.
A VCS is basically a program which keeps 'snapshots' of your code every time you tell it you've changed something. A useful VCS allows you to look at any snapshot you want. They also make sure not to waste space when snapshotting, e.g. if a file wasn't edited in a snapshot then it isn't copied, since it exists in a previous snapshot. These are just a few of the advantages of using a VCS like Git instead of just making copies of your code every now and then.
NOTE: Git is NOT a backup program! Backups should be made to external & offsite drives. Git might fulfill part of the functionality of a backup application, but it's not meant for it, so don't use Git for backup purposes!
If you're interested in Git and want to understand it more deeply, you might like to check out Tom Preston-Werner's 'The Git Parable'. My VCS explanation was taken from the first part of his fantastic parable.