To move along, either physically, or in a direction
toward the reaching of any type of goal,
even an emotional one, or toward learning something,
by very small incremental progress that is barely noticeable, but does proceed.
Being very very cautious and careful, to choose only certain words,
when addressing a particular topic,
And to tip-toe around it,
to try to avoid turmoil and to stay within a hopefully purposeful direction and a non-offensive way, that will not make waves or upset anyone's day!