The show How I Met Your Mother began in 2005 and is nearing it's end today. It centers around Ted Mosby who is telling the story of meeting his wife, and the mother of his children, to his kids. The kids are played by Lyndsy Fonesca and David Henrie and began the show already in their teens.
The reason some of the footage of them is reused is because after nine years they look and sound much older. They are supposed to be in their early teens while listening to the story, but the actors are actually 26 and 23 respectively!
Little is known about the kids on the show, such as their names. All that we do know is that Ted met their mother, had them, and wanted to name them Luke and Leia after Star Wars. Who their mother is was recently revealed, but whether he actually named them Luke and Leia, remains to be seen!
<a data-cke-saved-href="http://how-I-met-your-mother.wikia.com/wiki/Ted" href="http://how-I-met-your-mother.wikia.com/wiki/Ted" s_kids'="" target="_new">(Source)