Some HR staff ask if you're interviewing in other places, and some ask to be kept informed of changes in your job hunting process.
I suppose "changes" could mean you're no longer on the market because a job offer was accepted or because you decided not to change jobs after all. "Changes" could also mean it's looking like an offer could be imminent due to how quickly you've progressed through a series of interviews.
I usually answer honestly: yes, I'm looking at other companies too (because who isn't). But for changes in status, it's a little ambiguous about what they want to be updated about and when. Maybe next time I'll ask.
Anyway, given that they made the request, I assume they don't want to know every little detail, but maybe they do want to know something. Since they made the request, and if the intention was to be kept up to date, not just no longer looking, what do they want to know and when is it a good idea to contact them?