The intellect is the ability to know. The intellect is our capacity to generalise knowledge from our experience. When we see lots of red things as a young child we eventually learn that there is a colour called ‘red’. This allows us to grasp concepts that go beyond the purely physical.
The intellect seeks truth. When something is experienced we can reflect on it and try to understand all or a part of it, the concepts we form are always the best idea we have of things. This is why Aquinas says that “truth is the equation of thought and thing” (St Thomas Aquinas). Ultimately we seek to know God. Since God is the creator and source of reality knowing Him is to know the ultimate truth. Our intellect will never be satisfied until we know God.