Radak: It was when he brought the Aron from Beis Oved Edom ha'Giti to Ir David, and he gave it to Asaf and his brothers to sing it in front of the Aron. The first 15 verses are in Divrei ha'Yamim I, 16:8-22, with small differences. Here, David wrote it and elaborated to tell about Zera Avraham until they entered Eretz Yisrael. There (verses 23-33), it adds "Shiru la'Shem Barachu Shmo?" (Tehilim 96:2-13). For 43 years, they sang the former in the morning, and the latter in the afternoon, until Shlomo brought it to the Beis ha'Mikdash (Yalkut Shimoni Shmuel II, 142).

Malbim: After blessing Hashem for His conduct with man, especially healing the Nefesh and its reward, and conduct of the world in general according to the nature established in six days of creation, he comes to thank for miraculous conduct with His close ones.

Radak: He tells the singers and the Tzibur.

Malbim: It is His close ones, who received individual benefits.

Radak #1: Pray to Him. This is like "uv'Shem Hashem Ekra" (116:17).

Ibn Ezra, Radak #2: To teach ¹ people His way, like "va'Yikra Sham Avram b'Shem Hashem" (Bereishis 13:4). This is like the verse continues "Hodi'u va'Amim Alilosav."

'Rashi' (Divrei ha'Yamim I, 16:8): Call to Him to help His Aron. This is like "u'Krasem b'Shem Eloheichem va'Ani Ekra b'Shem Hashem" (Melachim I, 18:24).

Gra (Divrei ha'Yamim I, 16:8): Attribute all that you do to Him, like the Avos did - "va'Yikra Sham Avram b'Shem Hashem" (Bereishis 13:4).

Rashi: His deeds.

Radak: His actions against the Pelishtim due to the Aron.

Gra (Divrei ha'Yamim I, 16:8): It is the great Chesed that he conducts with Yisrael. He gives good to a Yisrael, then takes it away to atone for his sin in this world.

Malbim: They are conduct and deeds according to His Midos - "Rachum v'Chanun v'Rav Chesed" (Shemos 34:6), which is according to people's deeds, and reward and punishment.