Born into poor nobility (hence 'chevalier'), Lamarck served in the army before becoming interested in natural history and writing a multi-volume flora of France. This caught the attention of Le Comte de Buffon[?] who arranged for him to be appointed to the Musée d'Histoire Naturelle in Paris.
After years working on plants, Lamarck was appointed curator of invertebrates -- another term he coined. He began a series of public lectures. Before 1800, he was an essentialist who believed species were unchanging. After working on the molluscs of the Paris Basin, he grew convinced that transmutation occurred over time. He set out to develop an explanation, which he outlined in his 1809 work, Philosophie Zoologique).
His theory rested on two "observations" which nearly all scientists of his day accepted:
With this in mind, Lamarck developed two laws;
Thus, change in environment brings about change in "needs" (besoins), brings change in behavior, brings change in organ usage and development, brings change in form over time - and thus transmutation of a species.
Lamarck saw spontaneous generation as being ongoing, with the simple organisms thus created being transmuted over time (by his mechanism) becoming more complex and closer to some notional idea of perfection. He thus believed in a teleological (goal-oriented) process where organisms became more perfect as they evolved.
Modern science should not vilify Lamarck as it does. At least he believed in organic evolution. At the time there was no other theoretical framework to explain evolution. He also argued that function precedes form, an issue of some contention among evolutionary theorists at the time.
On the other hand, the inheritance of acquired characteristics is now widely refuted. August Weismann disproved the theory by cutting the tails off mice, demonstrating that the injury was not passed on to the offspring. Jews and other religious groups have been circumcising men for hundreds of generations with no noticeable withering of the foreskin among their descendants. However Lamarck did not count injury or mutilation as a true acquired characteristic, only those which were initiated by the animal's own needs were deemed to be passed on.
Nowadays, the idea of inheriting characteristics that were acquired during an organism's lifetime is called Lamarckian, which has become almost synonymous with 'false'. The environment cannot cause hereditary changes, according to the current orthodox view. However, recent work by for example E. Jablonka and M.J. Lamb, seems to show there is some room for a sort of 'Lamarckian' evolution, which goes by the name of epigenetic inheritance.
Charles Darwin praised Lamarck in the third edition of The Origin of Species for supporting the concept of evolution and bringing it to the attention of others. Indeed, Darwin accepted the idea of use and disuse, and developed his theory of pangenesis partially to explain its apparent occurrence. Darwin and many contemporaries also believed in the inheritance of acquired characteristics, an idea that was much more plausible before the discovery of the cellular mechanisms for genetic transmission. (Darwin, incidentally, acknowledged his theory would remain somewhat incomplete if the mechanism for inheritance could not be discovered.)