The phrase "to live for" means to dedicate one's life towards achieving a particular goal or pursuit. It implies that someone has a strong passion, desire or purpose in their life which they are fully committed to and focused on. This could be something as simple as living for the love of family, friends or hobbies, or it could involve striving towards more lofty goals such as achieving success in one's career or making a difference in the world through charitable work. Essentially, "to live for" means to have a sense of purpose and direction in life that drives and motivates an individual to make the most out of their time on earth.