When all of the ingredients inside a food are "kosher", the food is then labeled as "kosher." Pizza consists of 3 main ingredients: Dough, Sauce, and Cheese.
The ingredients used to make the dough (flour, sugar, salt, water, etc.) must be (and typically are) kosher. The ingredients used to make the sauce (tomatoes, tomato sauce, oregano, basil, salt, sugar, etc.) must be (and typically are) kosher.
The final ingredient, cheese, must also be kosher. Kosher cheese is made the same way as non-kosher cheese, except they don't add any ingredients that may be labeled as non-kosher.
There are several factors that determine if an ingredient is not kosher:
Since most ingredients that go into dough, sauce, and cheese can be kosher, kosher pizza usually tastes the same as non-kosher pizza. One final (and big) difference about kosher pizza, is that meat and dairy products are not allowed to be mixed (or eaten) together. Therefore, kosher pizza restaurants are not allowed to use real Pepperoni, Chicken, etc. as a topping, and typically go with a soy/tofu alternative.