Diverticulosis is when pouches develop in the wall of the colon in which stool can collect and eventually become infected. Most people (in Western societies) eventually develop it (our low fiber diet is generally thought to contribute to it). Many never have any symptoms at all, some report diarrhea, constipation, a "fluttering" sensation in the lower abdomen, pain in the lower left abdomen, changes in stool.
If pouches become numerous in a section of the colon or infection develops, the condition is called diverticulitis. Symptoms are the same as above, but more severe, and can also include nausea, loss of appetite, fever.