We have all been asked this question by a new photographer - my most recent conversation was at a wedding - and as usual I gave the answer " A standard focal length prime lens with a wide aperture ".
My own first photographic experiences were based upon this as it was the only option available then - zooms were horrid and dodgey at the time - and I learned my craft/trade/art/hobby/horrible mistakes using that one lens. As it happened, that lens was one of the sharpest ones ever made for the camera it fronted, and I never realized how good I had it until I moved on...story of our lives, isn't it?
Well, the story for the new photographer who asked is going to revolve around this lens. She's got a perfectly good Nikon DSLR with the kit lens...also perfectly good...and this will be the equally perfect key to portraits for her family.
It is the Nikkor AF-S DX 35mm f:1.8G. It's been out for years and has not had to be revised from the original recipe - the taste was great to begin with. It has never been an expensive lens, either.
I used it with the Nikon APS-C cameras in the studio for dance pictures and found it to be fast and razor-sharp at full-length shots. Closer in, the depth of field of a 35mm focal length was kind to the head and shoulders portraits while still keeping that sharp focus. The fact that it was physically light was a bonus - I was starting to flag at a certain point dragging an 18-200 lens everywhere.
In fact, if a person had a Nikon DX DSLR body of any sort, and wanted one lens to use for a year...and was determined to use only that lens...I think they would finish the year a far better photographer than when they started. Then they could go back to the kit zoom and learn more things at different focal lengths.
As terrible as this may sound in a column designed to get you to come in and spend money for photographic equipment, that year of discipline would make for greater success in the future. Umm...let's save the retail situation by saying that you could spend some money on a new tripod and bag...