Homestar, a combo deck is any deck that relies on getting certain cards out that work VERY well together and tend to kill the opponent. I cannot tell from your post what you were playing against, but it does sound like the Ironworks deck a friend of mine plays in MD5 block format...
It uses fast mana Chrome Mox, Talismans, and Pentad Prism to drop Ironworks quickly, then sacrifices things to play and activate Myr Incubator removing all the artifact lands (the only lands in the deck) and some other artifacts if necessary. Instead of the Fireball you died to, he then uses Goblin Charbelcher, or if neccessary simply attacks with the tokens. The end result is basically the same though...
I can think of a lot of examples of combo decks, many of which I've played. A rather broken example would be this one, which I posted on the CPA a while back...
4x Dream Halls
3x Intuition
3x Mind Over Matter
4x Mana Vault
3x Time Spiral
2x Paradigm Shift
4x Opportunity
4x Frantic Search
4x Stroke of Genius
4x Counterspell
4x Force of Will
4x Arcane Denial
17x Island
An opening hand might go:
Island
Mana Vault
Stroke of Genius
Island
Opportunity
Force of Will
Island
Let's say I go second. I draw a card and it's Dream Halls, drop an Island and a Mana Vault and say go. Then second turn I draw Counterspell and drop another Island and tap out to play the Halls. Then I pitch the Force of Will to play Opportunity drawing: Island, Frantic Search, Mind over Matter, and Island. I pitch Counterspell to play Frantic Search drawing Paradigm Shift and Island. I discard two Islands and gain UU as well, then pitch Shift to play MoMa and discard my two remaining Islands in my hand to untap the Mana Vault and draw mana from it, then I Stroke for 5 and draw Intuition, Mana Vault, Dream Halls, Island, and Frantic Search. I pitch Dream Halls to play Frantic Search and draw Opportunity and Dream Halls, then discard Island and Mana Vault and gain UU. Now I pitch Dream Halls to play Opportunity drawing Mana Vault, Island, Mana Vault, and Paradigm Shift. So I pitch Paradigm Shift to play Intuition and choose pick all 3 Time Spirals. So I pitch all of my other cards to draw mana from the Vault. I have 9UU and cast Time Spiral floating 5 so that I get a new hand:
Stroke of Genius
Mind over Matter
Dream Halls
Island
Frantic Search
Force of Will
Island
AND have 5UU in my mana pool after untapping my lands from the Time Spiral. At this point I have effectively won the game, since I can Frantic Search again for more mana and pitch the rest of my hand to Stroke of Genius for (counts cards after Frantic Searching on Appr.) 18 cards, easily enough to infinitely recycle my library using Paradigm Shift and Stroke of Genius to gain infinite mana and deck all of my opponents all on the 2nd turn...
Granted, tournament legal combo decks are not so viscious, but in Type I or even 1.5 some of them can still be as fast, though usually not as consistently. Combo decks have been responsible for the Type I restrictions of such cards as Dream Halls, Yawgmoth's Bargain, Memory Jar, Mind over Matter, Tolarian Academy, Burning Wish, Mind's Desire, Windfall, Doomsday, Voltaic Key, Lion's Eye Diamond, Crop Rotation, Lion's Eye Diamond, Tinker, and possibly a few others.
I don't really know what combo decks are used in Standard right now, but I do know the Ironworks deck is the favorite combo deck for MD5 block.
But basically, a combo deck is one which rather than trying to use fast cards and stomp the opponent as quickly as possible (aggro) or use defensive measures to incapacitate the opponent (control) attempts to get certain key cards into play that when combined have ridiculously powerful effects for the opponent.
Does that answer your question?
