The short answer is: you can do anything with a spindle that you can do with a wheel. A wheel lets you do it about three times faster, though.
Some expert spinners say that a spindle is better for spinning fine (laceweight) yarn and a wheel is better for producing sweater weights. But this is just a generality: by using the right size spindle and adjusting your speed, you can make worsted on a spindle, and by adjusting your wheel, you can spin finer yarn.
I have only been spinning for a couple of months, exclusively with spindles, and I find it very different from knitting. It's more physical, more sensory. You need to pay attention when you're spindling but you don't have to think: it's a great stress-reducer.
For an introduction to spindling, look for youtube videos by Abby Franquemont -- she's one of the best. Or get one of these books:
Spinning in the Old Way by Priscilla Gibson-Roberts or Spin It by Lee Raven. Or check the Spindlers group on Ravelry.