Pivots are great for controlling your movement within the initial dash animation. when you start a dash, until the initial dash window ends (the same window you have for dash dancing) your options are jump, grab, shield, dash attack, or do a basic turn around pivot. notice that you cannot do any attack out of dash that you want, nor can you crouch like you can out of a run. since roy has a relatively long initial dash animation, he would normally be required to wait out that time frame before being able to crouch, and thus put out attacks other than grabs or dash attacks. however, if you pivot during the dash animation, it basically puts you into your normal standing "idle" position, allowing you instantly do whatever attack you want. with this, you could dash forward, tilt the control stick backwards to pivot (which can be done any time in the initial dash), then put out a fsmash (flick the c stick any direction), as opposed to having to wait out the entire duration of the initial dash to put out an attack. its good for opponents that are just barely out of range of your sweetspot, where doing a full dash is way too much.
btw the input for doing a pivot is just a tilt backwards. whereas a DD will be caused by a "tap" backwards, the pivot is caused by a "tilt" backwards.