This is a good question answered in many famous stackoverflow boards.
But I think I can do better.
Let's quickly decompose what the numbers even mean. Usually, there are three, but there is no such hard limit. So a package might have numbers a.b.c .
Here a tracks the major updates, almost changing something fundamental about the package, b tracks minor updates, the introduction of a new feature or the removal of a major complaint, while c tracks minor patch fixes, nothing significant changes when this number of the package updates. Some even have numbers beyond this, but they are too trivial and mostly used by the development team itself.
So if you see in the dependencies field of a package.json file, the ^ and ~ characters are used to specify version constraints for the packages that are being installed.
The ^ character, also known as the "caret," is used to specify which versions are compatible with the current version of the package. For example, if a package has a version of 5.0.0, and you specify a version constraint of ^5.0.0, this will allow the package manager to install all versions of the package which are at least 5.0.0 all the way up to just below 6.0.0, meaning 5.3.9, 5.9.9 or even 5.99.99 will be downloaded and integrated into the project if available.
The ~ character, also known as the "tilde," is similar to the caret, but it is far more restrictive. It specifies a range of versions that are compatible with the current version of the package, but it only allows patches to that version. So if instead of ^5.0.0 we have ~5.0.0 , it will not go above 5.0.99, meaning it will only accept 5.0.1, 5.0.8, etc, but not 5.1.0 or anything higher.
Overall, the ^ and ~ characters are useful for specifying version constraints in package.json because they allow you to specify a range of compatible versions, while still providing some control over the types of updates that are allowed.