Weapon Skins were available to a limited extent in the first Killing Floor, but the idea really expanded with Killing Floor 2. Weapon Skins only change the appearance of weapons, and do not alter their stats.
If you drop a weapon with a skin applied, other players are able to use that weapon during the match, even if they don't own the applied skin.
In the first game, Weapon Skins were limited to just four DLC packs:
Each pack contained a skinned version of four different weapons from the base game. Once you purchase a pack, you could then get the skinned version of the weapon from the Trader. The shop would list the regular and skinned version of a weapon separately, but once you purchased one they would both disappear from the list (so for example, you couldn't have a regular AK47 and a Golden AK47 at the same time).
Killing Floor 2
In the second game, there are many more weapon skins available. Most are obtained from USBs (or Crates in the Console versions), but they can also be obtained directly from the in-game store or Steam Marketplace, as well as from Vault Crates, Prestige, and as Weekly Outbreaks Rewards.
You now select your Weapon Skin from your Inventory before starting a match, and then when you buy the weapon from the Trader it will automatically have your chosen skin applied. Even Knives, HMTech Healers, and Welders can have skins applied.