[@CollectorOfMyst] Sure, and I imagine the others can help explain.

Long time ago the Jews had a kingdom in Israel.  The Greeks under Antiocus IV sacked the Temple there when the Jews refused to stop their own religious practices and act reverent towards a statue of Zeus that he put up.  Eventually the Jews that fled banded together and came back, and though they were a smaller force they managed to kick the Greeks out again.

When they went to re-sanctify the Temple, and rekindle the light that is always kept burning there, they could only find enough consecrated oil to last for a single day, and getting more would take eight days.  But the oil lasted for eight days, and that was the miracle of Chanukkah.

The lamp or candelabra you're talking about has nine branches.  Usually it's called a menorah, but this is actually a generic term for a lamp of such a sort.  Most of the ones seen in Jewish symbolism have seven branches -- six and then the one that is used to light the rest (called the shamesh).  THe one used for Chanukkah is instead nine-branched, one candle for each of the eight days and then the shamesh.

The game with the four-sided top is called dreidle (or dreydel, or...you get the idea).  Gelt is often mentioned.  This used to be actual money, but now it's usually chocolate coins.

Fried foods are traditional, because you fry stuff in oil.  Originally this was sufganyot, or jelly donuts, but nowadays latkes (potato pancakes) seem to be better recognized.  Gifts are often exchanged, though the tradition varies by family.  In America it's made into a bit of a production, I think primarily because Christmas is such a production.  In Israel, I understand that candles are lit, there's maybe some singing, maybe a bit of dreidle, maybe a small gift or two, but it's really just a normal day.

There's a lot of stuff online if you want more information.  ^.^  My mom would come into my grade school to do a presentation each year, which was pretty great.  And I adore, ADORE latkes.  I do not get them enough.