Has anyone used HDFC concierge service that comes with diners club or infinia cards? I wonder what's that for and where can they help me.

I wonder what's that for

https://www.paisabazaar.com/credit-card/concierge-services-a-perk-for-premium-credit-card-users/ I've not used it, so cannot give any reviews.

They will make hotel bookings, flight bookings etc for you over a call

I see, have you used their services? Can they arrange airport-pick/drop?

I'm not sure, but it seems possible. Just call them up and ask. :) I've used flights and hotels, they will also help you redeem your reward points while booking.