For knots with a hyperbolic complement, there is a complete hyperbolic structure and for that structure there is a maximal peripheral torus that is flat, that is, with an induced Euclidean structure. The table gives the length of the meridian and longitude on the torus. If there are other short curves on the torus, these are listed here. The notation gives the number of meridians and longitudes represented by the curve, along with its length.
The data is taken from Knotscape, which itself is using Snappea to compute the values, and orientation issues are still being checked.