What are they and do I need them?
You probably don’t need them. In fact, unless you have a habit of corrupting the data on you hard drive you should probably go into File -> User Preferences -> Files and turn down the number of copies Blender is keeping (I turned mine all the way to 0).
What are they?
Those files are back up copies of your work (the higher the number at the end of the extension the older the copy)
Do you need them?
Only you can answer that, they can act as a version control point or as simple back-ups but, only you can really decide if you need them.
How do you access them?
To access the back up files you will need to rename them using the proper [.Blend] extension. For example: to access [Queen.Blend4] you would need to rename it to something like [Queen_4.Blend].
What should you do with them?
Unless you really think you need that many versions of your files I recommend deleting the [Blend2], [Blend3], and [Blend4] files and then changing your user preferences to only save 1 backup. If you really want to use a built in feature for version control then the auto incrementation feature will work much better for that.
Thank you very much for such a big answer. I probably confused a fields in
user preferences when I was trying to set up ammount of undo’s. Deffinetely
I dont need them. Thanks for your help