what does "lifting" mean? I see in certain places "lifting computation" or "lifting" mentioned. I haven't been able to accurately define for myself what is meant by that.

This usually comes up in computer science context. Any ideas what it means?
Computer science (especially theory B) has many connections to category theory, and that is the usual context for lifting. The basic idea is that you might have two objects $X$ and $Y$ that interact in a very intuitive way for you, and so it is easy to define a good morphism $f: X \rightarrow Y$. You might have a more complicated object $Z$ that is easy to relate to $Y$, but it is not obvious how it relates to $X$. So you will look at a morphism $g: Z \rightarrow Y$ and then use category theory to lift $f$ to $Z$ using $g$. 



In other words, you will find a morphism $h: X \rightarrow Z$ such that $gh = f$. For more info, see these slides.