The short version is that some guy got pulled aside for a patdown at some checkpoint, and the man's children had been in close contact with him, and so they got pulled aside for extra screening as well. We'd be more specific, but no one seems to know where or when or to whom this happened.
The reason the children were patted down is TSA agents have rules that they have to follow lest they get fired, and those are some of the rules. The reason those regulations exist, in turn, is because the Department of Homeland Security set them, after having been given the power to do so by the federal government of the United States of America. As sociologists and political philosophers will explain to you, the federal government for its part derives its legitimacy from a combination of facts and norms stretching back to before the Constitution was ratified. Maybe we should go into that, to help move this unprecedented scandal along.
Listen. These stories are boring and people should stop writing them. Terrorists have used children as suicide bombers and have planted explosives on pregnant women. If you have a (mostly) one-size-fits-all airport security system like we do, you have to take those things into account.
Now of course we could give agents wide discretion instead of making them explicitly follow the letter of every rule. But we don't do that because we don't trust them to use their common sense. Everyone knows that TSA employees are perfectly lovely and dedicated and blah blah, but the agency is notoriously underfunded compared to other parts of the government, and Congress keeps cutting its budget more, and the result is that screeners sometimes get recruited via job ads on pizza boxes. When we let them make their own decisions, they make bad ones.
If you want to change that you can either increase TSA's budget, so it can hire employees with decent judgement, or dismantle the agency completely, and then no more pat-downs for little kids ever. What you shouldn't be allowed to do is trash TSA without offering any alternatives, since down that road lies underpaid, over-controlled, not always bright frustration. See here for a rant from 2012 on the subject, here for one from 2013, and here for another from 2014. There are about a dozen more sprinkled across the site.
Here's the video. A couple kids who aren't even forming memories yet got lightly patted down by friendly, professional adults who kept them mostly at ease in full view of their parents. Come on. People aren't actually outraged over this, are they?
[Photo: khanzahir100 / YouTube]