Electric Shock or Current is a result of flow of electrons from your body.
When we touch a body/matter which is positively charged or negatively charged and when we touch it tries to become neutral which results in flow of electrons from our body to the matter or vice versa hence we feel the shock/current.
So in short the tiny shock you feel is a result of the quick movement of these electrons. You can think of a shock as a river of millions of electrons flying through the air. Static electricity happens more often during the colder seasons because the air is drier, and it's easier to build up electrons on the skin's surface. In warmer weather, the moisture in the air helps electrons move off of you more quickly so you don't get such a big static charge.