What is quantum decoherence and why does it matter?

[EvelynR]

I keep hearing about quantum decoherence in discussions about quantum computing and quantum mechanics interpretations. What exactly is quantum decoherence? How does it relate to the measurement problem? And why is it important for understanding why we don't see quantum effects in everyday life? Does quantum decoherence solve the measurement problem, or just explain why quantum effects disappear at larger scales?