Mini Wood Lathes are categorized as lathes with center to center distance in the range of 10-14 inches depending on who you ask. They're limited to turning small pieces that aren't too heavy since the motor will usually have less than 1 hp often less than 1/2 hp. One of the most common uses for mini lathes is pen turning. With an appropriate chuck they could also be used to turn a small bowl or plate.
The biggest advantage that a mini wood lathe would have over a larger tool is the low cost of entry. For a couple of hundred dollars you can purchase a small lathe that will last you for years and allow for a wide variety of projects.
One of the most popular mini lathes is the Shop Fox W1704 which is a very affordable but well designed and constructed lathe. You can read a review here.