The leaves started to turn color.

Literal

Leaves [subject-が] color-attach-begin.

色付く ('to take on color / begin to color') is a compact intransitive compound: 色 ('color') + 付く ('attach, take'). Used for fall foliage, fruits ripening, cheeks flushing — a vivid one-word expression for a gradual color change. Paired here with the auxiliary 始める ('begin'), it captures the precise moment leaves first start turning.