Radak: They are deep craters full of water, like "la'Afikim vela'Ge'ayos" (Yechezkel 6:3), "Al Kol Afikav" (Yeshayah 8:7). The water is [a metaphor for] the afflictions and dangers they had.

Radak (Shmuel II, 22:16): It is water that is drawn forcefully. All places where water is drawn forcefully are called Afikim for this reason.

Rashi: When the Yam Suf was split.

Radak: This refers to one way Hashem saves. (For the second way, refer to 18:17:2:1.) (a) When a person is drowning in great water, Hashem widens the water, and the Afikim are seen and the foundations of the world, which were covered with water, are revealed. This is via Hashem's rebuke of the water - "va'Yig'ar b'Yam Suf va'Yecherav" (106:9) - and from the breath of His nose, which dried the water ¹ . This is a metaphor for defeating the enemy in war, and David is saved.

Rashi (from Shemos Rabah 21:6): The depths were cleaved. When Yam Suf split, all waters in the world split.

Malbim: Hashem shattered the clouds to cease the thunder, but this led to a new affliction - a great flood, to the point that water flowed forcefully and the foundations of the world were revealed. I.e. in the six days of Creation, water covered the entire world. Hashem's rebuke sent the water and revealed the dry land; now, His rebuke returned the water to cover the land; also David was taken by the raging flow.

Rashi: It is from the strength of the blowing of wind of His nose.