This is the 3773rd most frequent Japanese word.
ときおり
Occasionally; from time to time.
The word 'ときおり' here is used as an adverb to express occasional frequency of the action '散歩に出かけます' (going out for a walk).
私は、ときおり散歩に出かけます。
I occasionally go out for a walk.
Here 'ときおり' signifies a periodic occurrence of the described action '昔の歌を口ずさむ' (humming old songs).
彼は、ときおり昔の歌を口ずさみます。
He occasionally hums old songs.
In this sentence, 'ときおり' indicates irregular intervals at which rain occurs, applied descriptively to a natural phenomenon.