The basic idea of a tensile test is to place a sample of a material between two fixtures called "grips" which clamp the material. The material has known dimensions, like length and cross-sectional area. We then begin to apply weight to the material gripped at one end while the other end is fixed. We keep increasing the weight (often called the load or force) while at the same time measuring the change in length of the sample.
The result of this test is a graph of load (amount of weight) versus displacement (amount it stretched). Since the amount of weight needed to stretch the material depends on the size of the material (and of course the properties of the material), comparison between materials can be very challenging. The ability to make a proper comparison can be very important to someone designing for structural applications where the material must withstand certain forces.