I know this question may be off-topic on academia SE, but really am not sure where to ask. I was admitted to a great PhD program recently, and was also invited to participate in their Open House in March. I was informed that I would be reimbursed for travel expenses. However the email says to book flights as early as possible to "qualify for a more competitive rate". Does this "rate" refer to the ticket price or the rate at which I am reimbursed? I'm afraid to ask the secretary since I don't want to make a bad impression.
Yes, yes it does. The hard part for you is that you need enough financial capacity (credit card, usually) to float cost of the airfare until you actually take both the flights. The university won't be able to reimburse you until you've actually taken both the flights. Even then, it may take them a month or two to pay you back. They won't pay your interest payments.
Basically, the email is telling you to book ahead because flight costs increase dramatically if you try to book too close to the actual travel date. For instance, for domestic flights within the US the cutoff is typically 21 days before the flight: ticket prices can become two or three times more expensive if you try to book after that point.
Of course, there's also the department's interest in having to pay less for your ticket, because that means there's more money available for other purposes (to pay for other students' tickets, hotel costs, meal costs during the visit, and so on).