A suicide mission is military operation in which few, if any, of the participants are expected to survive the mission. These are not to be confused with Kamikaze attacks used by the Japanese during WWII, as the participants will certainly try to survive, even if they are unlikely to succeed.
In most cases, these missions have a goal that is considered important enough that achieving it is considered worth the loss of the personnel assigned to the mission. As it is expected that the personnel assigned will not return, the mission plans often do not include a plan for the extracting of the personnel, but most missions will at least have a contingency plan for their survival and rescue. The best example of a suicide mission would be the famous Doolittle Raid over Tokyo during WWII.