Crown fell off and tooth decayed: Should I extract and get an implant?

I had a crown placed 2 years ago and it fell off about 3 months ago. The tooth holding the crown decayed. I was told by the dentist that the crown cannot be placed back and the molar would need to be removed. He also highly suggested an implant be placed so that my upper molar directly under the extracted molar, won’t move down and eventually fall out. Do you think this is a good idea? Do I really need an implant? Also, if when the tooth is extracted is it normal to leave some pieces of teeth from an extraction? What does the extraction actually entail?