Unit study homeschooling style simply put is taking a theme and learning all you can learn about that theme in all the subjects you wish for your children to study. For a basic example, you could pick the theme of prairies. For history you could study the time of the pioneers in the prairie, for lit you could read Little House on the Prairie, for science you could study the animals that live in and on the prairie or plants that grow on the prairie, for an artist study you could learn about an artist who primarily painted prairie scenes, for music history you could learn about music that came out of those who lived on the prairie, a field trip could be finding an environment near you that is similar to a prairie - you get the idea you can take basically any theme and create a unit study around the theme you chose. The sky is the limit on what you can chose and how deep you can dig into unit study learning. One major benefit of unit study learning is that your children will learn how to research a topic and the unit study style is perfect for families with multiple children as you can all study the same theme but gear the activities, books, and assignments to each child's learning style or age. Math and Grammar are usually covered separately and not tied to the unit study learning.
Many curriculums can fall into more than one style of homeschooling. Unit study style can be a hard style to nail down in curriculums alone. There are really only 2 that I know of that sell themselves as a Unit Study curriculum. These 2 are Five in a Row and Gather Round.
Five in a Row is an excellent curriculum it has been around for a long time and is one of my favorite young children curriculums. Five in a Row is a unit study curriculum based on literature books and is a fantastic way for children to learn.
Gather Round is new and has potential to be a crazy great curriculum. However, because it is a brand new curriculum that is being released one unit at a time I would be hesitant to pick this curriculum if my children were in upper elementary ages. There are no examples with Gather Round - we don't know how a student who uses this curriculum exclusively will academically turn out and I would not take the risk in the upper elementary ages. In younger elementary ages I think it would be worth the risk and honestly it can't hurt your child's academic progress that much. This is certainly a curriculum I will be watching in coming years and am hoping it is everything they have promised.
There are many other curriculums that are a mix of unit study, Charlotte Mason, and/or classical as well. The buttons below will take you to the website of these curriculums. The BLACK buttons are the 2 "true unit study" curriculums and the WHITE buttons are the mixed curriculums.