Luigi is Mario's younger, taller, twin-brother. He is often thought of as easier to scare, or less brave than Mario, but in almost everything else he is close to being an equal to him. He is usually helping his brother save Princess Peach, kart racing with him, and even having parties! He used to be a mere pallette-swap of Mario, but has since then evolved into a character with a unique personality.
Luigi's name came after Jumpman was renamed Mario. His brother came as an idea and his name was created because of a pizzeria near Nintendo of America called "Mario and Luigi's". He then made his first appearance in the 1983 arcade game "Mario Bros."
Luigi did not appear alongside his brother until the game Mario Bros., where he was simply a pallette-swap of Mario. (Interestingly, in the DK Jr. Introduction, there was 2 Marios pushing/pulling the cage. One of which, may have been a prototype for Luigi) That was their last arcade game in the Main Series. They would work together getting rid of creatures in the sewers by hitting them from underneath and then kicking them off the platform.
When Mario came to the Mushroom Kingdom to save Peach from Bowser, Luigi tagged along, although he was still a small pallette-swap of the main mustachioed plumber Mario. He helped save the Princess with Mario almost every adventure afterwards. Finally, once the Japanese only game Super Mario Bros. The Lost Levels, (Super Mario Bros. 2 in Japan) came around, Luigi got the ability to jump a little higher than Mario ever could. As this was a nice Ability, he got to keep it when Super Mario Bros. 2 (Super Mario USA in Japan) came to America.