Despite awkward comparisons made to pizza, omlettes or pancakes, okonomiyaki is a uniquely Japanese food that isn't anything like those foods, save for the fact that they start as a batter that is pan fried, and then loaded with toppings. However in terms of flavor, they couldn't be more far apart. It's been described as savory, which I suppose would be a fairly accurate way to describe them.
Okonomiyaki literally means "cook what you like" and when they go to an okonomiyaki-ya, customers get to choose their own favorite ingredients and then cook up their "pancakes" right at the table (which includes a grill). At many places they have a counter with a chef who will prepare an exquisite okonomiyaki right before your eyes (which taste much better the ones customers make, although it may be less fun). Because the customers choose their own ingredients, Japanese sometimes compare okonomiyaki to pizza, although the similarity really ends there.
The basic okonomiyaki will often consist of the "pancake" with cabbage grilled on the bottom and a good amount of katsuobushi (bonito fish flakes) are sprinkled on top. Special okonomiyaki sauce or basic tonkatsu sauce (similar to barbecue sauce) along with mayonnaise will often be spread on the top. Ingredients used will include, clams, pork, shrimp, beef, scallops, octopus, squid, corn, mixed vegetables, eggs, yakisoba noodles, and just about anything else you can think of.
The okonomiyaki style of cooking originated in Osaka and continues to be most popular there, although okonomiyaki-ya can be found throughout the country. The restaurants are popular with students on a budget, since the food is inexpensive, tasty, quite filling and fun to prepare.
Relevance to Urusei Yatsura
While the food of choice for the students of Tomobiki High has always been gyuudon, (with okonomiyaki being more important to the cast in Ranma 1/2) okonomiyaki has still made its share of appearances in the series. One example would be during a scene in UY movie 2 when the gang is discussing the end of the world at an okonomiyaki joint.