It's negative data. It's basically contrastive learning, except without backprop. Like you pass a positive example and then a negative example in each forward pass, and update the weights based on how they fired in each pass.

It's a really cool idea, I'm just interested if it's actually biologically plausible.

I might be wrong but inhibitory synaptic connections sounds like a neural connection with weight 0, i.e. it doesn't fire with the other neuron.