It depends what cells we're talking about. Thanks to insulin, glucose can be stored in the liver and muscle tissues as glycogen. In folks with poor insulin sensitivity these cells do not respond as effectively to insulin, and their uptake and storage is reduced, leaving more glucose in the bloodstream. In the obese, it's also likely the liver and muscle tissue glycogen stores are near max capacity. In this case insulin facilitates the uptake of glucose into adipose (fat) tissue through a process known as lipogenesis. When I wrote "insulin pushes fat into cells" that's what I meant.