How does the closure of M-type potassium channels by muscarinic receptors result in increased excitation of the target neuron?
Closing of the channel through muscarinic receptors involves activation of phospoholipase C and depletion of membrane phosphatidyilinositol-4,5-bisphospate which is needed for the channel to stay open. Once the channel is closed, potassium, which is a positive ion accumulates inside the cell eventually depolarizing it or lowering its threshold for activation. Thus, blocking the extrusion of K ions results in excitation of the target neuron.
See this for more: Brown, D. A., and Constanti, A. (1980). Intracellular observations on the effects of muscarinic agonists on rat sympathetic neurones. Br. J. Pharmacol. 70, 593–608.