The Songs of Ascent are fifteen Psalms. The meaning of ascent is much debated. Here is the most imaginative explanation brought to you courtesy of the Talmud.
“When King David was digging the Shitin [a stream that ran beneath the Holy Temple, into which the wine libations were poured], the water of the depths arose and threatened to flood the world. David said, ‘Is there someone who knows whether it is permitted to write [G‑d's] name on an earthenware shard and we will throw it into the depths and it will subside?’ . . . Ahitophel responded, ‘It is permitted.’ [David] wrote the name on earthenware and threw it into the depths. The depths receded 16,000 cubits. When he saw that it receded greatly, he said, ‘The higher the depths, the moister is the ground [which benefits agriculture].’ He said the fifteen [songs of] ascents, and the depths rose 15,000 cubits.”
Man, that King David sure knew how to make the Psalter work for him, huh?