Rashi: When the Mikdash was destroyed, birds nested there.

Rashi citing a Midrash: This discusses while the Mikdash stood; the Tzipor is Keneses Yisrael.

Radak #1: This was when David was in Eretz Pelishtim. Bamos were permitted; there were Mizbechos everywhere. Birds would nest in them. However, they did not nest in the Beis ha'Mikdash, due to Tum'ah. They even made something on the Bayis (Kalya Orev - Midos 4:6) lest birds rest on it. David said, I am not even like birds - they can nest on Your Mizbechos, and I cannot be there! The verse mentions Tzipor and Dror, which normally nest in settled places.

Radak #2: If this refers to Galus, it teaches that the birds find a place to nest on Your destroyed Mizbechos, and we cannot celebrate the festivals there and offer Korbanos.

Radak citing Shemos Rabah 20:6: Tzipor and Dror are a metaphor for Keneses Yisrael. They came to celebrate the three [annual] festivals in the Beis ha'Mikdash and offer Korbanos. Bnei ha'Galus say that they yearn to ascend like Yisrael used to do in their land.

Malbim: The verse depicts a Tzipor or Dror singing in Kano (its nest), like a Levi on the Duchan singing to Kono (his Creator). The chicks brought on the Mizbe'ach while the Mikdash stood, they are of this singing Tzipor; it is as if it brought its chicks for a Korban to Hashem on the Mizbe'ach. How happy are these birds - they already found Bayis and a nest, and the former offered its chicks. However, the Levi is like a bird that wandered from its nest; it is alone on the roof, and does not sing. So [the Leviyim] hung their harps on the willows of Bavel.

Rashi: It put.

Radak: They are young Kohanim who were always at the Mizbechos, just like chicks [are always] at the nest.

Radak: Even though I am in Galus, You are my King and my G-d.