The phrase "to hold the reservation" means to keep or secure a spot or reservation for something, like a hotel room or a table at a restaurant, so that nobody else can take it. Full definition
If you find a reservation you may want to book, you can hold the reservation for 24 hours instead of booking it to decide whether the fare is right for you. (upgradedpoints.com)
You should still hold some reservations about this prediction though. (myscizzle.com)
If you do try to book through the website, you can choose the flight but can not confirm or hold the reservation without miles. (liveandletsfly.boardingarea.com)