It means I'm not interested in doing something and/or don't want to do it. For example: "My co-workers are organizing a group to discuss new technologies and invited me to join, but I can't be bothered—it sounds very boring to me and a waste of time!"

It means that you have no energy or interest to do something, or that ypu are too lazy to do it I can't be bothered to get out of bed. I can't be bothered to do my homework. You can find out more here: http://dictionary.cambridge.org/dictionary/english/bother I hope that answers your question. Let me know :-)