They are exactly what is known as "Berliners" in Germany - donuts without a hole (unlike most American donuts), with a jelly (i.e., jam) filling. They are traditionally eaten in Hanukkah, because the tons of oil they are fried in (this makes them taste so good...) reminds Jews of the re-consecration of the temple - what we celebrate in Hanukkah - because it involved miraculous appearance of oil which was needed to light the holy lamp in the temple. Oil which was enough to light the holy lamp for 8 days, today is barely enough to fry one Sufganya :-) The word "סופגניה", sufganya, comes from the verb "ספג", to absorb, i.e., it absorbs all the oil.
Actually, in America we'd call them chocolate-covered jelly donuts. I totally agree with your point about the ridiculous transliteration. People are taking this DL course to learn Hebrew. And here we have a Hebrew sentence with a new word סופגניות. What are סופגניות? Why, they're "sufganiyot"! Didn't that help? This whole section is filled with this insular, self-referencing approach to Jewish holidays, so that if you're not already literate in Judaism, you've got a steep learning curve ahead.