Halo 4 offers a variety of things to unlock in its multiplayer mode, otherwise known Infinity Multiplayer, which is split between Spartan Ops and War Games. Among the things you can unlock are weapons, aesthetic armor types, skills, and emblems.
Emblems are little logos that you can use to personalize your Spartan. When you kill someone, they’ll see your player card, which contains your emblem, level, and other pertinent information. As you level up, you’ll gain new emblems to unlock for which you can use to designate who you are in the game. Your enemies may come to fear you as “the guy with the bow-tie cat emblem”.
To that end, Redditor and Halo fan lol-jk has compiled all of the emblems into a chart so you’ll know precisely when these emblems will be unlocked. Keep in mind that these are only for the foregrounds, and not for the backgrounds.
You’ll gain these emblems at whatever SR or specialization it says on the chart. The stuff listed in “other” can only be attained through achievements or as pre-order bonuses.
Halo 4 is currently available for the Xbox 360 as an exclusive to the platform. Microsoft and 343 Industries have no plans to release the game on the PC or any other platform, so you’re going to have to pick up an Xbox 360 if you want to play the game.