Rarity is a rough measure of the quality and scarcity of an item. Items of higher rarity are typically have some extensive difference from a Base item, but are harder to find and more expensive to craft.
There are 5 rarities: Base, Common, Rare, Epic and Legendary. Each rarity has its own color, based on Warcraft's gear system, and can be recognized by the color of the gem at the center of the card's portrait when opening Loot Chests, face down items above common quality will be displayed with an appropriately-colored glow when hovered over its hexagon shaped portrait.
There are skins of every rarity, with the Base skin being the default, Rare skins being simple recolors, Epic skins being more advanced recolors and sometimes simple outfit changes, and Legendary skins being complete outfit changes and sometimes including alternate interaction with other heroes or extra voice lines, or completely different voiceover.