Yes, your customers can have their own account on the portal, sign in whenever they like and see the trips they have already booked with you.
When someone registers, the portal keeps a small profile for them with their contact details and the travellers they book for most often, such as a partner or their children. On their next visit those details can be filled in for them rather than typed again, which speeds up the payment step and cuts down on spelling mistakes in passenger names. Their past bookings sit behind the same login, so they can open an old trip, check the booking reference and download the ticket or hotel voucher again without ringing your office.
There are limits worth knowing about. A booking your staff makes for a customer who phones in will only show in that customer's account if it is linked to the account at the time, so it helps to ask for the email address they registered with. Whether a customer can cancel or change a trip on their own from that screen depends on your settings and on what the supplier allows, and many agencies prefer to keep that switched off so every change passes through their own team. Anything the supplier does not send back to the portal, such as a seat added later at the airport, will not appear there either.
Register as a test customer yourself, make a booking and then look at the account screen exactly as your customer would see it, and decide before you go live how much you want them to be able to do there without your help.