3-9X40 would make an object to appear 3 times to 9 times larger than actual size. The larger the objective lense is the more light it will permit to enter your eye all other things being equal.
The clear diameter of the objective lens, divided by the magnification = the exit pupil diameter (size of light beam coming out of the ocular lens). Your eye can only open up enough to use a 7mm exit pupil - anything larger than 7mm is wasted!
EXAMPLE: An 8X56mm scope will give you 7mm of exit pupil, ALL of which your eye can use if completely dilated. A 4X with a 40mm objective gives you a 10mm exit pupil, of which your eye can only use 7mm (MAX) when completely dilated.