When you go to the Kosel HaMaaravi you will see an abundance of birds in and around the area. It wasn't always so. The roof of the Bais Hamikdash had spikes to prevent birds from sitting on it. Now that the Bais HaMikdash is destroyed a bird, who can lay its eggs anywhere, can even make a nest on the Makom HaMikdash where the Mizbei'ach once stood.
The bird is a reminder of our fate in Galus. Klal Yisroel has only one place to serve Hashem. The Bais HaMikdash, our entrance way to heaven, is no longer accessible to us. Unlike the birds in galus we have no place to call home. (Mahari Ben Yichiye)
"Gam Tzipor Matza Bayis U'Dror Ken La Asher Shasa Efrocheha Es Mizbichsecha Hashem Tzivokos Malki Veiloikoi"; Even the bird has a home and makes its nest on the Mizbei'ach of Hashem.