“To toe the line” figuratively means to conform, submit to authority, obey the rules. The expression started out literally meaning to put your toes against a marked line. It has been used in the discipline of sailors and in sporting events with a starting line among other things. It dates from the 1800s, when “to toe the mark” was also a common expression.
“To tow the line” is not a common expression, but it would mean to drag a rope or something similar behind you.
