mapStateToProps returns nothing but your app's state stored in the global store and passed to your component as props.
mapDispatchToProps wraps your action creator in the redux's dispatch method and pass it again as a prop to your container. So basically the global store's state and action creators wrapped with dispatch are all together passed as props to your component. You are passing state and the redux's dispatch method as a prop to the component.
mapDispatchToProps = dispatch => ({
    dispatchAnAction: dispatch(actionCreator1)
})
Here the connected component say ComponentA will receive the props and one of the prop will be dispatchAnAction which is returned by mapDispatchToProps as in the above code. You will call the dispatchAnAction like this this.props.dispatchAnAction() and the action returned by the actionCreator1 will be dispatched to the global redux store.
P.S If you are starting wth redux this course is highly recommended.