double types are a powerup (usally 3rd on the power bar in most gradius and gradius related games) and allows your ship to fire an extra shot in certain direction depending on what type of double you use. here is a list of some of the double types to get other edits off to a start
gradius:
double: another shot is fired 45 degrees up
gradius III
double: another shot is fired 45 degrees up
tail gun: another shot is fired directly behind the ship
vertical: another shot is fired directly up
a small qiurk with doubles however is that when double is activated it usally cases less shots to be fired in the default direction because only so many shots can be on the screen at once. this causes players to usally choose laser over double