What does this equation mean?

At the circuit level, each neuron unit holds a membrane potential, implemented as a charge on a capacitor or a value in a small register, that accumulates incoming weighted spike inputs and simultaneously leaks — decays exponentially — toward a resting value between inputs. A standard discrete-time version of this leaky-integrate-and-fire rule is $V_m[t+1] = V_m[t] + \sum_i w_i s_i[t] - \frac{V_m[t]}{\tau}$. where the $s_i$[t] are the incoming binary spike events, the $w_i$ are the corresponding synaptic weights, and τ sets how quickly the leak dissipates unused charge. When $V_m$ crosses a fixed threshold, the circuit emits a single digital pulse — a spike — on its output, and its membrane potential resets. Nothing is emitted, and in an efficient asynchronous implementation nothing is computed downstream, in any cycle where the threshold is not crossed.