Answer:
The Germanic homelands in northern Germany and Scandinavia were overpopulated so the tribes began searching for more lands for more resources and for more agricultural purposes so they could feed their families. The Roman Empire was right next door and offered these amenities. Furthermore, Rome itself was cash-strapped and had spent far beyond its means and was increasingly short of both money and manpower to fight its hostile enemies on its borders. Basically it had stretched itself far too thin, so therefore the Germanic tribes that began to cross into Roman territory couldn't have started coming at a worse time.
Additionally, many of the soldiers serving in the Roman legions were actually Germanic mercenaries who were recruited. Many of these soldiers later returned home to their tribes knowing Roman ways and styles of fighting, which helped later on when they fought the Romans.
