Lamarck’s theory exclaimed that organisms changed during life in order to adapt to their environment and that those changes are heritable (parents will pass them on to their offspring). What makes the biggest difference comparing to natural selection is that he believed that the changes are made by organisms' desire.
Darwin’s theory (natural selection) disagrees with the influence of animals’ desire on evolution. Darwin explains that variability exist within species and that some traits are more suitable (favorable) to the environment because help an organism to survive and have more offspring. Favorable traits are heritable. Unlike Lamarck, Darwin believed that evolution doesn’t happen according to any sort of plan.