So before explaining what insulin does, you need to be aware of the fact of what homeostasis actually is. Homeostasis is the maintainance of a relatively stable environment within narrow ranges. One of the homeostatic mechanisms involves the regulation of blood glucose level, and two hormones (protein-based) are involved in this maintained equillibrium; insulin and glucagon. Both of these hormones are produced by the pancreas. Insulin is synthesised in beta cells of the pancreas, while glucagon is synthesised in the alpha cells of the pancreas.
When blood glucose level is too low, and is out of the narrow range of which is it homestatically regulated at, glucagon is synthesised by the alpha cells. The glucagon is then transported via the blood-stream to liver/muscle tissues, or effector muscles/cells, telling them to break down the glycogen into glucose. Remember back in biomacromolecules, glycogen is a complex carbohydrate polysaccharide made of branched chains of glucose monomers. When the glycogen is broken down, glucose is released into the blood stream, increasing the blood glucose level to then be within the homeostatic range of blood glucose level, which I think (correct me if I'm wrong), is betwen 3 and 4.
When blood glucose level is too high, the beta cells synthesise insulin. This protein based hormone is synthesised and travels via the bloodstream to the muscle/tissue cells to send a message to them to increase the rate of removing glucose from the blood and storing it as glycogen, when glucose forms into this polysaccharide in the condensation reaction. By doing so, blood glucose level is lowered until it is met within the narrow range that homeostasis dictates.
So rather than thinking it is immediately insulin or glucagon which causes an increase/decrease in blood glucose level, they are merely chemical messengers that act on the muscle/liver tissue target cells to either remove glucose from the blood and store it as glycogen, or break down glycogen in catabolism in order to then release it into the bloodstream and increase blood glucose level.
Hope this helped