The phrase "award space on the route" refers to the availability of seats or tickets that can be booked using award or loyalty program points or miles for a specific travel route or flight. Full definition
There is very little award space on that route, but there is some if you're flexible like I am. (milevalue.com)
There is award space on this route basically every day. (milevalue.com)
Unfortunately those days are over, and it's now quite literally impossible to get Swiss first or business class award space on any route from North America to Europe except their Montreal route. (travelsort.com)