Why Tehilim?
Dovid HaMelech ע''ה (King David), authored the Tehilim. He composed these songs while in danger, wandering in the deserts from his enemies and also during times of joy and light.

In his Psalms, Dovid joined the tribulations of his people with his own.  When he petitioned for himself he petitioned for the entire nation, for he identified well with their suffering and with their joy.

Through these psalms Dovid drew closer to G-d.  it has become customary for Jews to grab the sefer Tehilim at those times when one needs to reach out to Hashem for salvation or for praise.