To be more precise, select a coordinate system in 3 dimensional space by chosing three mutually perpendicular axes (the x, y and z axes) with the same unit length on each axis. The cubic lattice is just the set of all points in space that have integer coordinates. Two lattice points are called adjacent if the distance between them is exactly 1.

A walk is a connected path in space that consists of straight lines between adjacent lattice points (one imagines walking around with stride length 1 and only stepping on lattice points). A walk is self-avoiding if you don't cross the same lattice point more than once. A walk is called closed if it ends where it begins (this is allowed for self-avoiding walks too).

So a closed self-avoiding walk on the cubic lattice forms a knot - quite often it is the unknot, but sometimes it is nontrivial. Such knots are called cubic lattice knots.