A sufganiya is a puffy, ball-shaped donut with some sort of filling. They are very popular in Israel, and are one of the foods most associated with the celebration of Hanukah.
My family has always eaten jelly donuts for Hanukah. This year, I finally thought to try and find out why... It turns out that there is no great story behind the jelly donut/sufganiya tradition. Fried foods are popular on Hanukah, since it is, after all, a celebration of holy oil. Donuts are not only fried, but also delicious. Really, if you are going to celebrate, would you rather do it with a small, goo-filled cake or a latke? (Well, if you're smart, you'll do it with both, but you get my point).
The Sephardi have long had the tradition of making fried fritters, and by the 1930s German Jews were making pfannkuchen* -- essentially a jelly donut. They carried the tradition with them when they emigrated to what is now Israel. In a splendid ebullience of good taste, the people of Israel elaborated on this tradition, and while the 'traditional' sufganiya is filled with jelly or jam and sprinkled with powdered sugar, these days you can find them filled with anything from caramel to Roquefort cheese. Raspberry Jelly is still holding its own as a popular filling, and is what my family always gets (but then, we're American, and would be hard pressed to find a donut filled with pineapple cream even if we wanted to). Modern sufganiyot can also be iced with various frostings, the most popular of which is chocolate.
But wait! What was that word I just used? Sufganiyot? Well, Hebrew does not form plurals in the same way as English does; the plural of sufganiya is sufganiyot. (But If you were using the Yiddish word ponchke, you would be quite right to add an 's' to form the plural). There is some debate as to the correct pronunciation of sufganiya and sufganiyot; SOOF-gan-EE-yah SOOF-gan-EE-yot are probably safe attempts, but as I personally speak no Hebrew, you should not take my word for it. (TheLady recommends soof-gah-nee-YAH).
There is also some debate as to the roots of the word sufganiya. Some say that it comes from the Hebrew word sfog, meaning 'sponge' (or the related Hebrew word safag, meaning 'to absorb'). Others claim that it comes from the Greek sufgan, which (they say) means 'puffed and fried'. Apparently there has been at least one book on Hebrew etymology which made this claim, but I have been unable to find anything to support this. It is unlikely that this second etymology is true. It may, however, be that the sufganiyah takes its name from the sufganne, a fried lump of dough that has been eaten in the Mediterranean since before year 0 (CE), and which may have had Greek influences.
* Pfannkuchen can also refer to pancakes (AKA Eierkuchen). If you're traveling in Germany and want a jelly donut, you should ask for a berliner (Northern Germany) or a Krapfen (Southern Germany).
Thanks to TheLady, Apatrix, and sloebertje for help with all these foreign words.
If you like sufganiyot, you might also like the Polish paczki. (A goyim tradition in the same vein as sufganiyot).