I had hoped to present a simple explanation of various knot polynomials, but I'm not sure that's possible. Bridge representations are fairly easy to explain, though. Each knot or link has a minimal bridge number. A bridge is a section that goes over other sections. The above representation of the Borromean Rings has three bridges.
Many knots require only two bridges, though.
In 1949, mathematician H. Schubert presented what is now known as Schubert's normal form . The 19 comes from the length of each bridge. I started with a line, then divided it so that I could number the ends with 0 and 19. Then I copied this bridge elsewhere, upside down. Well, start with 0, and start travelling.