Why do some smaller boats have very tall masts?

So I was looking at a dock with several boats and noticed that many of them had very tall masts.  I don't know very much about boats, but was a bit confused about why it was necessary that they even have masts at all because wouldn't they have motors?

At first I found out about vestigial masts on larger ships.  For example warships nowadays are probably not using sails but apparently some still have masts to mount radar and other antennae.  On a smaller scale, but still fairly large, 50+ foot yachts may have forward masts to mount lights.

In my attempt to wade through the boating information I quickly discovered that there are many terms I don't know... 

Keep in mind though, that as you reduce the tack angle below 90 degrees (making the clew to luff horizontal distance shorter than the foot length) you often wind up having to install jacklines along the lower luff which ease the slugs or slides off just to be able to raise, lower or reef the sail.

What the what.  At times I was a bit over my head.

Without being able to find much information I came to the conclusion that I was probably asking the wrong question.  Thinking about it some more, sails and motors didn't have to be mutually exclusive.  It probably made sense that a sail boat with a large mast would also have a motor to help out when the winds weren't very strong or for ease in undocking.

Searching a bit more it seems like it's not uncommon for sailboats to have a motor as well for the reasons I thought of above.  So I was probably just looking at a bunch of sailboats... doh.