Comfort fit means that the inside of the ring is rounded, which helps it slide over your knuckle easier. The inside diameter of the ring gets bigger as you get closer to the edge of the ring. In contrast, standard fit rings are flat on the inside of the ring, which means the inside diameter is the same as you move along from one edge to the other. Because of this difference, comfort fit rings tend to fit a bit looser than standard fit rings of the same size. As a general rule of thumb, when purchasing a comfort fit ring, you should choose a size that is about a half size smaller than your standard fit ring size.
Another thing you can do to make sure you have the best fit, visit a local jewelry store. A typical jewelry store will have ring sizers that come in 2 different millimeters. One is usually 5 or 6mm wide and the other is 8mm. You should have your finger sized with the narrower one. The comfort fit on our bands require this or the ring will likely be too large. Even if the ring you are purchasing is wide you should still use the narrow one. There should also be a slight degree of resistance when going over the knuckle.
See this chart for a DIY way to size your finger.