Atropine is a muscarinic antagonist, which means it opposes the action of acetylcholine at muscarinic receptors (M1, M2, and M3). It binds reversibly at these receptors, so I can be outcompeted by more acetylcholine.
Atropine is mostly known for its treatment of bradycardia (slow heart rate) and for ophthalmic uses. Since acetylcholine acts on M2 receptors in the heart to decrease heart rate and atrial contractility, atropine can do the opposite - speed up the heart rate and increase atrial contractility. The pharmacologic pathway for this is acetylcholine binding at the M2 receptor, which is a Gi protein coupled receptor, inhibits adenylyl cyclase, which then converts less ATP to cAMP, leading to less activation of protein kinase A and eventually a lower concentration of calcium ions in the heart. Atropine will reverse all of these, increasing calcium ion concentration.
In the eye, acetylcholine acts on M3 receptors (Gq via phospholipase C) to constrict the pupil and contract the ciliary muscle, which stretches the lens to bring objects into focus (accommodation). Atropine will therefore dilate the pupil and freeze the ciliary muscle, making a person's vision bright and blurry, but making it much easier to look into someone's eye.