An F-stop indicates how many light the lens could theoretically transmit - focal length divided by diameter of aperture. In practice, there are some losses each time a light ray enters or exits a glass surface. In a lens with many elements, these losses may sum into a considerable amount (like 25% loss in some old zoom lenses). This, naturally, affects exposure.
T-stop takes this transmittance into account and shows how much light a lens can really transmit. For example, a Nikkor 70-200mm f/2.8 VR II appears to be T/3.2 - it can transmit the same amount of light as an F/2.8 theoretical lens could. This discrepancy is not a design fault, but rather a fact of life.
The concept of T-stop is especially important for videography, as a person watching a video would notice the scene getting suddenly darker/lighter if changing lenses would result in a different T-stop not compensated adequately by shutter speed (even if F-stop stays the same).
Since there is always loss and never gain of light, T-stop of a lens is always slower than F-stop, almost equal in best cases. The difference between T-stops vs F-stops of lenses has declined with the evolution of coating technologies.
The T-stop is only important in context of exposure. When estimating depth of field, F-stop should be evaluated.