These were a social species of ants (apparently there are more than 12,000 species of ants - one of those facts that always take me by surprise, even though I've probably heard it before), and it seems they have teams, with a scout ant and 3 to 8 forager ants in the scout's team. In the experiment, the scout explores a maze and finds some honey, then the scout communicates this to the foragers and the foragers can then find their way to the honey.
The experimenters measured how long it took the scout to communicate the information to the team and showed that bigger mazes required longer to communicate the directions. Specifically, with mazes constructed as binary trees with N nodes, N a power of 2 (4, 8, 16...), so, the information required to get to the right node would be log2(N). (The instructions would be the sequence of left or right decisions for each fork in the tree.)
They claim to have shown that the time taken to communicate the information was of the form
t = t0 + t1 log2(N)
In other words, an overhead time of t0 then t1 for each bit of information.
They then did experiments with mazes with a different geometry: a corridor with rooms off to one side. This time they showed that it took longer if the honey was further away, at rooms near the end of the corridor, rather then close to the entrance. Perhaps the most bizarre result, though, came from what they did next.
With this corridor geometry, they ran the experiment lots of times with the food more often in a couple of specific rooms, say room 7 and room 14. After a while, the ants were quicker in communicating the fact that the honey was in one of the 'usual' rooms than in a different room (so now it was quick to say it was in room 14, even though that was towards the end of the corridor, for example). But, the clever thing, if they put the food in a room near to one of the usual rooms, that, too, was quick to communicate. So, for example, if in room 13 they could effectively communicate "the room before the second usual room", or room 12 would also be quick "two rooms before the second usual room".
Thus they claim that the ants can count and do simple addition and subtraction!