From Halopedia, the Halo wiki
Armor effects are a special customizable option in Halo: Reach, the Halo: The Master Chief Collection edition of Halo 4, and Halo Infinite. Armor effects are visible in all gametypes, though they are not displayed in cutscenes.
On November 16, 2020, when Season 4: Reclaimer was released for Halo: The Master Chief Collection, it made the effects available for use on Sangheili player models in Reach. On June 23, 2021, with the release of Season 7: Elite, these effects were added into Halo 4 as a new customization option.
Halo Infinite would feature player effects in a major capacity, following their absence in Halo 5: Guardians.
Halo: Reach and Halo 4
Armor effects functioned as passive character model effects, visible to other players in-game. They served no purpose past being aesthetic changes. Certain effects such as Heart Attack, and Pestilence featured specific death effects, which activated as the player died, such as a flurry of hearts floating above the player's place of death. Others, such as Legendary and Eternal were only active as the player remained alive, with no specific death effect associated to them.
Originally, Halo: Reach was the first and only Halo title to feature armor effects in any capacity, with the original releases of Halo 4 and Halo 5: Guardians forgoing the option. However, in 2021, Halo 4 would be updated to feature Reach's suite of armor effects within The Master Chief Collection. They functioned identically to their Reach counterparts.
Following their absence in Halo 5, and their reintegration into Halo 4, Halo Infinite would feature armor effects in a notably more major capacity. Unlike Reach and Halo 4, which featured armor effects that could be passive, activated on death, or both, Infinite would divide effects into three defined categories: Armor Effects, Mythic Effect Sets, and Kill Effects.
Armor effects act much like they did in prior titles, being passive, aesthetic changes to the player's character model. Unlike Reach and 4, these effects didn't feature any death effects, with their presence being solely limited to when the player is alive.
Mythic effect sets are passive effects that affect the player's character model's actions, such as footsteps, and slides. They can also be activated through the use of certain equipment, which varies by the effect. These can be used in tandem with different armor effects, and aren't defined by them, unlike prior titles.
Kill effects take the place of death effects in prior titles, and are a part of weapon customization. Following the theme of armor and mythic effect sets, kill effects are activated when the player kills another, and unlike prior titles, are defined by the killer's choice of effect.
Mythic Effect Set