Albedo
An albedo, sometimes may wrongly refered as diffuse map, is a term used to describe reflection coeficient of a material surface containing view-independent Base Color information without any additional lighting or shadow information. Often stored into a Image Texture.
It's used to tell which color tint and initially add basic details for a Diffuse surface. And defines what we normally think of a texture as being before enhanced by other "treatment" textures like bump maps or specular masks.
Engine
Engine-wise, Albedo is usually used to archive a brighter or toon-like surfaces, such what we see in 
Dota 2 and 
Team Fortress 2 characters. Often confused and interchange term for Lambert Diffuse texture, often combined with other informations such radiosity maps, luminance maps, shadow maps, diffuse maps and occlusion maps as cheap shading aproximation.
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