The picture below shows a typical nerve in the body. When you want to make a muscle contract your brain sends a signal down the nerve (indicated by the yellow arrows travelling down the nerve). Once the signal reaches the end of the nerve it stimulates the release of a chemical called acetylcholine.
Acetylcholine (the blue circles in the diagram below) travels across the gap between the nerve and the muscle and binds to a small receptor on the muscle side of the gap. When acetylcholine has attached to the receptor a cascade of reactions occurs resulting in the contraction of the muscle.
When anti-wrinkle product is injected it sits in the end of the nerve as shown in the diagram below. It can take between 5 and 14 days for the anti-wrinkle product to fully accumulate in this space which is why there is a delay between having injections and relaxation of lines. The anti-wrinkle product blocks the release of acetylcholine from the end of the nerve and the muscle does not receive the message to contract. Without contraction of muscle the lines are reduced.