During the Guardian Games in Destiny 2, you will see which of the three classes are the best of the best. To do this, you need to participate in various activities and speak to Eva, who you can find at the center of the Tower in front of the Guardian Games Podium. A primary objective many are attempting to complete is to collect Laurels during this event. You can earn Laurels for your class, and some from other classes.
What do the Laurels of other classes do? Overall, these add to your totals for various bounties or Guardian Game Medals you are attempting to complete. You usually earn these during PvP matches, such as when participating in the Crucible. If you are nearby an ally Guardian when they earn a Laurel by doing one of the objectives, like taking out an enemy with a grenade, a charged melee attack, or a super, you earn them as well.
The Laurels of other classes do not count for as many points like the ones you earn for yours. For example, if you earn Laurels on your Hunter by taking out an enemy using a grenade, you will receive three points for the Guardian Games Medal you have in your quest log. When your ally Guardian takes out an enemy in the same fashion, and you earn their Laurel, your total only goes up by one point. You cannot rely on other ally Guardians to continually raise your point status, but it does help, especially if your Laurels are assisting them at the same time.
They don’t do too much, but it does make grinding Laurels a little bit faster when participating in the PvP events or any of the strikes in Destiny 2.