What do scientists mean when they describe a “single-stranded” versus a “double-stranded

What do scientists mean when they describe a “single-stranded” versus a “double-stranded” molecule of DNA? Can DNA go back and forth between being double and single-stranded? If so explain how and does its sequence change? Will DNA replication process always create identical strands? Why or why not? What would the consequence of a “mistake” be?