So the essential difference is how the threads within the fabric are arranged. A woven fabric is made up of two sets of straight threads (warp and weft) at right angles to each other. It's made on a loom. A knit fabric, on the other hand, is made of a series of looped threads and is made by using needles to essentially loop the yarn around itself. This means the knit fabric, regardless of fiber composition, is going to be stretchier because the loops can stretch in all directions. The woven fabric can only stretch, and only minimally, along the bias, because the horizontal and vertical threads are already pulled taut when the fabric is made. Therefore, woven fabrics are much less flexible but also have more structure.
This page has a visual example.
ETA - the example of knit on that page is only one type of knit. It's the most common, called stockinette stitch, with a distinctive stitch pattern that looks like stacked v's. But there are other types of knit stitches, but the common factor is that if you pull them taut, you will see a series of loops.
