A fete is an extravagant celebration or party, sometimes outdoors. It can also be considered a festival where a large number of individuals gather to honor someone. As a verb, to fete someone is to honor them with a large party. It makes feted and feting.
The French word from which fete is derived has a circumflex over the first e—to make fête—but the mark is usually dropped in English. Either spelling is correct.
The word come from the Latin festum which meant festival.