My answer is similar to Philip's... "involving" someone or something is to include them in an action or process where as "including" someone or something is simply to add them to a list or group. Here's an example: "My closest friends were all involved in planning a surprise birthday party for me but somehow they forgot to include my boyfriend in the guest list."

Include: to include something is to make something part of a whole. "With this definition, I will include an example of its use." - "The parts of a car include the body and engine." Involve: to involve something (or someone) is to make it part of a situation or event, for as a necessary part, maybe to achieve a result. "There is thinking involved in explaining the differences" - "The parts of a car include the body and engine, where combustion is involved in making it the engine work."