The cat up in the tree climbed down to me.

Literal

Tree [possessive-の] top [possessive-の] cat [subject-が] my [possessive-の] place [to-へ] came-descending.

降りてくる combines 降りる ('to descend, climb down') with the directional auxiliary ~てくる ('come toward'). The combination means 'to come down toward the speaker,' capturing both the vertical motion and the speaker-ward direction in one compact verb phrase. へ is the directional particle for 'toward,' a slightly softer alternative to に for destinations.