Chestnut-sided Warbler photo by Charles Moores
I love basic questions like this where the definite answer is not known. We all know that birds migrate. We know why migration is a good idea, even though it's extremely hazardous. It's a good idea because it evolved. If it wasn't worth the risk, it wouldn't happen. There are other details, about food supply, weather, competition, etc. which are the reasons it evolved, but the fact is, it evolved. But why? Why is migratory behavior in some birds selectively advantageous? Some theories - pick your favorite:
1) At some point in time, environmental pressures induced some birds to move to find more food or to lessen competition for nesting sites. Pressures (or weather changes) in the new site may have forced them back. The cycle continued, and the birds that refused to move eventually died out as the migrant birds were more successful breeders and their genes predominated.
2) Advancing glaciers caused temperate zone birds to retreat to the tropics part of the year and return to their ancestral home when the glaciers retreated. Or conversely, retreating glaciers afforded tropical birds the opportunity to move to temperate zones to exploit food and breeding resources. Since glacier movement was not a yearly occurrence, this theory is generally not accepted, since it doesn't explain how the migration north/south cycle stabilized.
3) To me, the most plausible explanation is that groups of tropical species spread northward in warmer months to exploit new food and nesting resources to escape increased competition in their tropical homes. The temperate zones offered more daylight for feeding, and a wider range for selection of nesting territories. When the weather cooled, the birds returned to the tropics. Most bird families (taxonomically speaking) are thought to be of tropical origin, so this theory may hold true.
A nice mystery. We may never know the answer, but we enjoy watching the spectacle every spring and fall. There are many fascinating details about migration. I encourage you to find a resource and read more about it if you're interested.