In some Digital cameras ordinary batteries are not functioning. But it functions with alkaline battery why?

I don't quite understand your question, but lets say the camera takes AA batteries. The camera would work with any type of AA batteries as long as they are not run down. Alkaline batteries are usually specified by the camera manufacturers because they have more power and therefore will last longer - usually much longer. Some digital cameras are real power hogs.

Because the alkaline battery delivers more power.

What do you mean by "ordinary batteries" ?
I would say that to most people, alkaline batteries are ordinary batteries. I would expect more people to say that Ni-Cad or Li ion batteries would be more "exotic" than standard Alkaline batteries.