This is an old test thats being used less and less these days. Its done by adding radioactively labeled T3 (lets call it rT3) and a resin that binds free rT3, to the patient's blood sample. Remember that naturally the blood contains T3 bound to Thyroid Binding Globulin (TBG). This test actually measures the availability of binidng spots on TBG The more T3 the blood contains the more of it will be bound to the TBG leaving less spots on the TBG for the rT3 to bind and thus more rT3 will be taken up by the resin. So a high resin uptake suggests that all the spots on TBG are filled up which in turn suggest hyperthyroidism. The opposite is true in hypothyroidism when there are a lot of free spots on TBG and thus more rT3 binds to it and less is taken up by the resin.
As you can see this test depends on the amount of TBG in the blood and is this is the reason it is being replaced by newer and better tests.
If you chose not to remember the details just remmeber that a high resin uptake = high T3 in the blood, and vice versa