The term rainbow is used in all community card variations like Texas Hold’em to describe a board texture that contains no cards of the same suit.
For example, a flop of As7d4h would be described as a rainbow flop since the three cards on the flop are all of different suits (spades, diamonds, and hearts).
From the strategic standpoint, rainbow boards have a special place since they contain no flush draws. On these types of textures, the best flush chance a player can have is a backdoor flush draw (i.e., three cards of the same suit, needing help on both turn and river to complete a flush).
When talking about a full runout (all five cards), a rainbow board is the one where no flush is possible. So, there could be two hearts, two spades, and one diamond, and since there are no future cards to come, this is a rainbow board, as a player can't have a completed flush.