A hot material is one that is instanced in both the scene and the Material Editor. When you get a material from an object, that material is hot. Any changes you make to the hot material are reflected in the scene wherever that material is applied.
To edit a material without changing the scene, you can get the hot material from an object, then make a copy of it. The term for the copied material is cool.
White triangular tabs in each corner of the Material Editor sample slots show that the materials in those slots are hot.
In the Material Editor, the only time you need to select an object is when you're assigning a material to an object. When you're adjusting a material, object selection doesn't matter.