An incisional hernia happens when a weakness in the muscle of the abdomen allows the tissues of the abdomen to protrude through the muscle. The hernia appears as a bulge under the skin and can be painful or tender to the touch.
In the case of an incisional hernia, the weakness in the muscle is caused by the incision made in a prior abdominal surgery. To paint a clearer picture: during surgery, an incision is made in the muscles that make up the abdomen. For some reason, that muscle doesn't heal, so a gap opens up as the muscles tighten and release during activities. Instead of a flat, strong piece of muscle, you have a piece of muscle that has a small gap in it.
After a while, the tissues underneath realize there is an escape route through the muscle and they start to poke through the opening, to the point where they can be felt under the skin. An incisional hernia is typically small enough that only the peritoneum, or the lining of the abdominal cavity, pushes through. In severe cases portions of organs may move through the hole in the muscle, but this is much less common.