When we eat something, after munching and swallowing a bite, we are strongly stimulated to have one more bite. What is the taste that causes this effect?
As Reg Dwight comments, I don't think there's a particular taste which causes you to want more.
However, the food may be described as being moreish:
British • informal
So pleasant to eat that one wants more:
a moreish aubergine dip
It's derived from more+ish, which the ODO definition doesn't make clear, and pronounced /ˈmɔːrɪʃ/.
Something that stimulates our appetite could be said to be mouthwatering.
Appealing to the sense of taste; appetizing: the mouthwatering aroma of a baking pie.
Umami is one of the five basic tastes partially responsible for stimulating the salivary glands, i.e. the mouthwatering feeling we experience when we taste something savoury and to our liking.
(of food) causing a desire for more: these cakes are very moreish
palate: the sense of taste
palatable: having a pleasant or agreeable taste; pleasant or acceptable to someone
palatability: the hedonic reward provided by foods or fluids that are agreeable to the palate in regard to the homeostatic satisfaction of nutritional, water, or energy needs
I think you may be looking for umami. It's the lesser known basic taste, along with salty, sour, bitter, and sweet.
The taste comes from glutamate. In foods this is found most often in MSG (monosodium glutamate) form. Adding MSG to foods is one simple way to increase the umami flavor of food, but the flavor can also be found naturally in things like ham and parmesan cheese.
I've commonly heard that MSG (and umami in general) will cause an increase in appetite, but I don't know if it's actually true. There have been studies done to determine the real effect, but they seem conflicted. Some show an increase in appetite and others don't. At least one seems to indicate that it can increase the speed at which one "acquires" a liking for a new taste, and participants would eat more subsequently. Perhaps that's a separate question for Skeptics.SE.