Doing something sensibly means you've acted in a wise and reasonable way. The Department of Education sensibly announced a snow day after that huge blizzard last night!
Behaving in a rational way, using your intellect to make decisions, reacting reasonably to things — these are all ways to act sensibly. You might sensibly decide not to jump off a rope swing into a river until you've determined how deep the water is. Or you could sensibly choose not to debate politics with your hotheaded uncle. Sensibly comes from the Late Latin sensibilis, originally defined as "perceptible by the senses" and later also meaning "reasonable."