The boxes are "recyclable" in the sense that the same "box activation" (i.e. turning a box on) can be used to travel backwards multiple times without requiring the box to be reset. This is in specific contrast to the operating model assumed by Abe at the start of the story, in which he describes the boxes as "one time use only" because he believes that there is a single, unified timeline.
For example, if you were to set the timer for a box so that it powers on at 8:00 AM on Monday, then turn it off and get into it at 9:00 AM, so that you could travel back one hour, you would emerge at 8:00 AM, as you expected. However, you are now in an "offshoot" timeline that is different from the one from which you just traveled back. If, at 8:05 AM, you are looking at the powered-on box that you just came out of five minutes ago, it is "empty" in the sense that it doesn't, at that moment and from your perspective, contain your past you coming backwards through time. (This does not agree with the assumptions behind the rules for time travel developed by Abe, but there is plenty of evidence in the movie to demonstrate that there are multiple independent timelines.)
As an example: If you wait around until 9:00 AM, there will be another you (per the movie's lingo, your "double") showing up to get into the box. If you're planning to stick around in this timeline, it's preferable to avoid this encounter and to allow your double to do so, since then your double will exit this timeline and there will be only you left here. However, it's not required that you avoid this encounter. If you stayed around until 9:00 AM, you could probably prevent your double from entering the box. Congratulations! You have just created what seems like a paradox. But, let's ignore the philosophical implications and look at the box again. It's past 9:00 AM, and nobody has turned it off yet. There's your proof that this is a different timeline from the one that you left when you yourself traveled back to get here.
Suppose that, after your encounter, your double wanders off reflect on the novelty of meeting oneself... or suppose instead that your double has been conveniently drugged and locked in an attic by your actions. The box is still on at 9:30 AM. If you wait another half hour, it's still on at 10:00 AM. What happens if you turn it off at that point and get in yourself? Two hours later (from your standpoint), you'll be back at 8:00 AM, in yet another offshoot timeline. There will be a "double" of you here, as well, who is expecting to travel back at 9:00 AM -- just like the double that was there the last time you came through, and really just like you yourself were expecting 15 minutes after you first set the timer.
What if you wait half an hour, turn off the box at 8:30 AM and get in yourself? Your double will probably wander in at 9:00 AM and be surprised to find the box is not even on. But who cares? You can never get back to a timeline you've left, so it's all theoretical, anyway. From your standpoint, you've just gone back to 8:00 AM on Monday morning for a third time.
You've only ever turned on the box once. It's the "same" box in all three timelines. (This is where we discover that the definition of the word "same" is insufficient for dealing with the rules of reality as implied by the box.) But you've already used it three times from that single initial activation. The box will always be "empty" in any offshoot timeline, so it can be used to travel backwards again and again with just one box activation, by someone so inclined.
In the movie, Aaron and Abe are both struggling to understand and express their ideas of how the box works and its implications, so "recyclable" is the best way Aaron can describe the above. I don't think it's directly related to the fact that Aaron takes another box back with him when he discovers and uses Abe's failsafe -- this is just a way Aaron figures out to "smuggle" a working box back to a time before Abe has completed (or at least before he has turned on) his second box, which Abe intends to use for his own first trip back.