OK, here goes... (hope i get the explanations right in English. you're sure to find better ones in wikipedia)
Matza, plural matzot (modern Hebrew) or matzos (Ashkenazi dialect) is a special food of Passover - it's unleavened bread. it's to remind us of how when the Israelites / Children of Israel (the Hebrew people) left Egypt they had to hurry so they didn't have time for the dough to leaven.
for you non-Jews, basically it's a big flat kind of cracker. not particularly tasty. bad for your diet - too much of it causes constipation, and it's high in calories.
during Passover (approx a week) Jewes aren't supposed to eat bread, only Matzot.
the Seder is a holiday feast on the Eve of the Passover holiday. historically, it's modeled after Greek-Hellenic wine feasts. anyway it's a very ritualized meal, during which the Haggada is read. this is a cremonial text, discussing the liberation of the Israelites when they left Egypt. it's to remind us of our history and our liberation from enslavement in Egypt. there's lots of symbolism, there's particular foods that have to be on the table, special foods eaten only during this meal (and not other days), 4 wines of glass are drunk etc.
this Haggada is read through the ceremony. there's about an hour of reading (during which you only drink some whine and eat little bits of the symbolic foods at the appropriate places) before you get to the actual meal.
on the table there's some soft of cloth in wich are 3 matzot which are special (i mean they're ordinary matzot, but they're considered special) and aren't touched or eaten. early on in the ceremony the middle one is broken in two. this middle one is called Afikoman (or maybe just half of it, i don't know). anyway, one of the "rules" of the ceremony is that you haven't finished the ceremony and fulfilled your obligation, and aren't supposed to leave the table, till you've had a small piece of the Afikoman. that's more or less at the end.
so over the years a tradition has developed that the children "steal" the Afikoman and hold it for ransome. since the grown-ups can't complete the Seder till they've eaten of it, they have to give presents to the children. basically, the children are hijackers.
there are variations: some have the elder, who "runs the show", hide the Afikoman as a pre-emptive move against the theiving children, and then the children spend the evening looking for it. others just let the kids steal it easily, they (the kids) hide it and the grown ups go hunting for it (well, only pretend...they don't really try to find it).
as far as gifts go, Passover is the holiday of "big good gifts", like Christmas is for Christians.
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the land of Mordor, where the Shadows lie
M.C. Escher - Reptilien