What is "Gitis"?
Rashi: It is a musical instrument that comes from Gas. There were craftsmen there who make it.
Rashi (citing Shocher Tov 1): [The Mizmor] is about Edom, which will be trampled like a winepress 1 - "Purah Darachti Levadi" (Yeshayah 63:3).
Ibn Ezra, partially cited in Radak: He gave it to the families of Oved Edom ha'Giti [to sing it]; he was a Levi (Bamidbar Rabah 4:20).
Radak #1: It is one of the kinds of song (refer to 4:1:1:2).
Radak #2: David composed and said this when he was in Gas.
Rashi: The Mizmor does not seem to discuss Edom!
What is the purpose of this Mizmor?
Radak: It is praise and thanks to Hashem, and tells His mighty acts.
Malbim: It refutes philosophers who belittle man. They say, would a wise worker create Kelim of 10,000 Kikarim of silver for the sake of one iron needle - i.e. the giant celestial bodies for the sake of the earth (a tiny dot compared to them), and just for man, who is Batel compared to the earth?! Moreh ha'Nevuchim and Bechinas Olam refuted them. "Va'Yiten Osam Elokim bi'Rki'a ha'Shamayim Leha'ir Al ha'Aretz" (Bereishis 1:17)! All physical existence is only for the ideal person who will guard Hashem's commands. Nature is subordinate to him. The world rises, or can be nullified, based on his actions (Mitzvos or rebellion). This is the foundation of the Torah, reward and punishment. He is Hashem's portion in this world; He showed this via wonders in Yetzi'as Mitzrayim, Har Sinai, and when He dwelled in the Mikdash or Mishkan. He desired to dwell only here. The nation that guards His Mitzvos is His treasure. He called them every expression of endearment - His firstborn son, His betrothed bride, His nation and His inheritance. 1
Malbim: This investigation is primary and a foundation of our Torah, and the foundation of every religion. This is why we are not astounded at the personal Hashgachah on humanity. Also with this, we will knock the skulls of deniers who say that Hashem abandoned the land, and His honor is only on Shamayim. So claimed all nations that served the sun, and sacrifice to the celestial bodies.