For combo colours beatmapping rules, see: Ranking criteria/osu! and Ranking criteria/osu!catch 6g6h4f
Combo colours are colours which help separate combosets from another. Combo colours apply to all hit objects in a beatmap. When a new combo is started, the colour of combos changes to the next defined colour. The New Combo button can be found on the right side of the Compose tab in the beatmap editor.
Combo colouring is an important aspect to a beatmap's aesthetics, as it is one of the only ways to change the visuals of a beatmap besides storyboarding and skinning. Combo colours can be set in the Song Setup with a minimum of 2 and a maximum of 8 combo colours. Combo colours defined in a skin will only be used when a mapper does not define any combo colours, or when the player overrides it in their settings.
In osu!, all combosets have a colour. A new combo is started when the colour of the hit object changes. The colours will keep repeating themselves depending on how many the mapper defined (or how many your skin's skin.ini file defines).
In osu!catch, each fruit is coloured in the order given. Droplets and end-slider fruit will always have the same colour as the start-fruit. However, bananas will always have a tint of yellow.