The common misconception is that celery contains "negative calories." All foods contain calories. The way you must look at it is how many calories does one stalk of celery contain, versus how many calories it takes to digest it. According to the nutrition data website, one 8 inch celery stalk contain about 6 calories. Many people believe you actually burn that off when chewing. Though celery does take a rather conscious effort to chew, chewing burns about the same amount as watching the grass grow. The calorie loss is going to be during the digestion of the celery.
Celery is actually loaded with latent energy, but the plant's composition only allows us to metabolize a small amount. The latent energy is packed tightly in the form of cellulose; a complex sugar which humans are unable to metabolize. It's not that the celery is difficult to digest, but rather it provides fewer calories than what is needed to digest it--so the overall effect is "negative calories."
Keep in mind, the amount of calories you lose is very minimal. This is not the miracle diet food. The amount of calories lost will probably be no more than 10-12 calories a day. The good thing is celery can quickly satiate your hunger, preventing you from eating other high-calorie foods.