Being a good listener is important when it comes to making and continuing conversations, but repeating what the other person just said can also help you to seem more engaged. As author Eric Barker explains in his book Barking Up the Wrong Tree:
Social skills expert and author Leil Lowndes recommends simple repetition.

Via How to Talk to Anyone: 92 Little Tricks for Big Success in Relationships:
…simply repeat—or parrot—the last two or three words your companion said, in a sympathetic, questioning tone. That throws the conversational ball right back in your partner’s court.

It shows you’re listening, interested, and lets them get back to telling their story.

You’ve got to be slightly savvy about this one but it’s surprisingly effective.

Surprisingly effective?

Yes, it is.

It is?
Barker also noted that research has shown how repetition is effective in hostage negotiations as it helps in building rapport.

Obviously, you don't want to do this too often during a conversation, lest you really end up sounding like a parrot.