Grid cells : Between what is the correlation of autocorrelogram measured?
Autocorrelation is calculated between the spikes-histogram and itself. 

The experiment is carried out while the activity of a specific neuron is recorded.


Histogram - An animal runs in a circular arena which we divide into multiple squared bins, whenever the cell fires (i.e. generate an action potential) 1 counter is added to the location (the bin) in which the animal is currently located.
Autocorrelation - Two instances of the spikes histogram are observed such that one is "placed on-top of the other" and the correlation between the two instances is calculated.  


When the two instances are perfectly aligned, their
autocorrelation is 1 (they perfectly match).
Now we start moving one of the instances. The match between the two instances is not perfect (the autocorrelation is smaller than 1) but because there are peaks (at the spikes-histogram) all across the arena, if we shift one of the instances such that it would be "on top" of another peak (e.g. each peak is aligned with the peak directly to its right) the autocorrelation would, once again, equal 1.
(τX,τY) - The shift of one of the instances is carried out for every value of x and y of the arena (i.e. for every phase) and the value of autocorrelation for each (τX,τY) shift of the first instance relative to the stationary second instance is plotted - this is what the autocorrelation figure shows.

What should we learn from the autocorrelation figure - That the cell response is indeed represented by a grid. The figure exemplifies that when the spikes histogram is shifted in a single full period (i.e. to the next peak) it fully matches itself, so the grid pattern indeed characterize similarly the whole arena (tessellating it).