No one knows for certain how the New Orleans dish that we know as "jambalaya" got it's name. Some say it is from the French word  'jambalaia', meaning a mish mash, or mixup, and also meaning a pilau (pilaf) of rice. 

The Dictionary of American Food and Drink offers this tale:
Late one evening a traveling gentleman stopped by a New Orleans inn which had little food remaining from the evening meal. The traveler instructed the cook, "Jean, balayez!" or "Jean, sweep something together!" in the local dialect. The guest pronounced the resulting hodge-podge dish as "Jean balayez."
No matter how the name originated, it is certain that jambalaya is a delicious and popular dish that goes perfectly with family gatherings and good times.

Old Louisiana bayou recipe

2 onions, chopped
4 tablespoons butter
1 can tomatoes
1/2 can tomato paste
4 garlic cloves, chopped
2 ribs celery, chopped
1/4 green pepper, chopped
1 teaspoon chopped parsley
3 cloves, chopped
1 pound boiled ham, diced
2 pounds peeled, boiled shrimp
3 cups cooked rice
Salt, black pepper, cayenne

Saute onions in butter 5 minutes. Add tomatoes, tomato paste and cook 5 minutes more. Add all seasonings, chopped very fine. Cook 30 minutes, stirring frequently. Stir in ham and cook 5 minutes. Stir in shrimp and cook 5 minutes. Stir in rice and season to taste with salt, black pepper, cayenne. Simmer 30 minutes, stirring frequently.

Recipe courtesy of Mrs. William P. Dilworth, Jr