Linear just means, "like a line." If something is linear, it is straight. It is often used to describe something that is free of peaks and valleys, consistent in its performance. This term is used in all aspects of electronics, and is generally a good trait.The term "linear amplifier" is also sometimes used to describe a wide band amp, one that isn't optimized or tuned to a particular frequency band but one that can operate from DC or very low frequency up into the high RF range.
Tube amps are those that use vacuum tubes as their active elements instead of transistors or FETs.