Vaginal exercise balls work out the muscles of your vaginal wall by providing resistance for them to contract against. Basically anytime you put anything in your special place, the vaginal muscles will automatically squeeze around it. In addition most vaginal exercisers have a small weight(s) inside that will roll around as you move. As this weight rolls around, it will roll against the vaginal wall at different places and cause increased contraction at that spot. So you can just put the ball(s) in and go about your business while getting a work out to boot, or you can do Kegel exercises (voluntarily contracting and releasing these muscles) with them in for an additional boost. This will keep your lady bits nice and toned which helps with bladder control (important later on in life), firms and tightens (especially important after childbirth) and makes your orgasms stronger. You also become more aware of your vaginal muscles and how to voluntarily contract them and with greater force, which a penetrative partner will likely really appreciate.
Exercisers with one ball provide the least amount of resistance and are the lowest level of intensity, with intensity increasing for each additional ball. There are also a variety of weights and shapes too. Which exerciser is right for you just depends on the intensity of work out you're looking for. Some have strings for easier removal, but anything you put in your vagina can't get "lost" inside you since your cervix prevents that, so the string is not strictly necessary. I have heard many complaints about the strings on various exercisers being uncomfortable, though I have not had this problem myself and appreciate being able to simply pull the string to remove versus having to dig a bit.
I have the Ami by Je Joue and I love it!! The Ami is actually a set of three exercisers of different weights and shapes, so you can work your way up in intensity or switch it up for a different type of work out.
I hope this helps clear things up a little bit.