1. Mark had no scruples when it came to romance. He would string some poor girl along until he found someone he liked better. Then he would drop the first girl without a second thought and leave her broken-hearted.
2. The crook strung the old lady along with the story that he was investing her money in something safe, when in fact he was stealing from her.

The expression is often used to describe what a false-hearted lover does to someone who is naive or unsuspecting (opt.1).