This is, of course, a perfectly reasonable question, and the answer, also of course, will depend upon whether the party is being thrown to celebrate Halloween or Holi - or, indeed, Christmas or a wedding or winning the Cup Final.
But, as it happens, the party in party-coloured isn't that sort of a party at all. An alternative spelling is parti-coloured, and that makes it a bit less surprising that party/parti in this case means partly one colour and partly another, or others.
The world is full of party-coloured things:
Japanese Chin Dog. Photo by Pointer8
party-coloured tights. Detail from The Tiumph of May by Francesco del Cossa, about 1470.
Rosa mundi. Photo by Libby norman
(To be party-coloured the colours need to be separate, not smeared or blended.)
So: what's the first thing you can spot?
Mine, very close to hand, was my yellow and white tea mug.
Spot the Frippet: something party-/parti-/coloured. Party used to mean of more than one colour. The word comes from the Old French, where it means striped, from the Latin partīre, to divide.
The word party meaning a social gathering comes from the same Latin word, which also came into English by way of Old French, this time as partie meaning part or faction.
Which tells you everything you need to know about parties, doesn't it?