Acetylcholinesterase is an enzyme which breaks down acetylcholine. If this enzyme is inhibited, the amount of acetylcholine will be higher.
Acetylcholine is a type of neurotransmitter that acts in a number of systems.
Acetylcholine is the neurotransmitter that passes between motor neurons and muscles at the neuromuscular junction. Thus, acetylcholine is needed to initiate muscle contraction. Usually, acetylcholine is rapidly broken down. However, in the presence of the AChE inhibitor, the muscle would receive a longer signal from the motor neuron, increasing the duration of the contraction. For this reason, AChE inhibitors can result in increased urine retention. As a result, AChE inhibitors are sometimes prescribed to help control overactive bladder.
Acetylcholine also acts on the parasympathetic nervous system. The parasympathetic nervous system innervates the smooth muscle of the GI tract. AChE inhibitor will result in sustained stimulation of this muscle. Similarly, sustained parasympathetic activation can result in bradycardia (slow heart beat).
Acetylcholine is also the neurotransmitter present in the sudomotor system (part of the sympathetic nervous system). Basically, these are the neurons which control the sweat glands. So an AChE inhibitor would result in a longer signal to the sweat glands and increased sweating.
So, to summarize, the effects of AChE inhibitors on the heart, bladder, GI tract, and sweat glands would be, respectively, bradycardia, urine retention, hypermotility, and hypersecretion.