This is a great song, the kind that sticks with you and almost compels you to sing along.
The lyrics are probably about two children, pre-teens, perhaps they live in the same neighborhood and perhaps have been playing together since they were toddlers. But they're growing up now and falling in love. Their parents warn them to "watch how" they play, since things are getting a little too physical for their comfort. The parents can't quite imagine their kids transitioning into sexual beings, especially since they've seen these two playing in the sandbox for all these years. The kids find they have to escape "into the night" to "hide what" they're doing. Because, after all, "what would they say if they ever knew".
The image of the kids running, holding hands, tumbling to the ground, indicates that the are still rather young, as does the opening line where the parents still refer to them as "children". This image of youthful love and first sexual experiences makes the song especially appealing as it harkens back joyful memories for many listeners.
Some interpretations you find on the web, including that the song indicates either a homosexual relationship or even incest between a brother and a sister are in my opinion misguided. The song is too cheerful to indicate something as sinister as incest. The lyrics do not indicate the gender of the kids so it could theoretically refer to any sexual orientation. However, I think the opening line's "watch how you play" makes "boy and girl" the more likely interpretation. I can see two parents saying "watch how you play" to a young boy and girl who are too physical when playing, but I would think that at the time this song was written in the 1960s the reaction would have been quite different if the parents saw amorous physical contact between two boys or two girls.
But the beauty of any good song is that people can project whatever they want onto the lyrics in order to connect with it, so if some of you in the gay/lesbian community out there want to see this as a first g* relationship song, it's certainly ok by me. I just don't think a careful reading of the lyrics supports that conclusion.