The projectile velocity is the speed at which a projectile flies.
When a system gives you weak vs. strong attacks, usually the stronger input indication will yield a faster projectile speed.
You use different speeds so that the opponent has to make a judgment about what its speed is. You want them to guess wrong, usually.
If your projectile is fast, it will reach the opponent faster, but the problem with this is that if it is blocked or dodged in any way, then your character will be stuck in a longer-exposed recovery than with the slow projectile (even if it’s the same amount of time! seriously. do the math), making it simpler for the opponent to counterattack.
For this reason, the slower-traveling versions of projectiles are much better to use as an offensive shield, or zoning, or for strings, in order to minimize the amount of time spent being vulnerable. Obviously, you still use the fast (strong) one if you need it to hit on time, or you need some other factor it offers (e.g. if you need your combo to knock out or knock down).
For example, consider a Haō Shōkōken in the King of Fighters series, where you may often roll through projectiles instead of blocking them: a slow projectile is easier to take note of but harder to avoid (because the timing has to be just right to dodge, and one still has to be mindful of what could come next); a fast projectile is harder to notice in time, but easier to avoid once noted (because the one who is dodging can just jump quickly, block right away and be done with it, or roll with less exacting timing).