In the context of programming language discussion/comparison, what does the term \"power\" mean?
Does it have a well defined meaning? Even a poorly defined meaning?
It can have several meanings. In the very basic sense there's power as far as what is computable. In that sense the most powerful languages are Turing Complete which includes pretty much every general purpose programming language (as opposed to most markup languages and domain specific languages which are often not Turing complete).
In a more pragmatic sense it often refers to how concisely (and readably) you can do certain things. Basically how easy is it to do certain tasks in one language compared to another.
What language is more powerful (besides being somewhat subjective) depends heavily on what you're trying to do. If your requirements are to get something running on a small device with 64k of memory you're likely not going to be using Java. Most likely the right language would be C or C++ (or if you're really hard core assembly). If you need a very simple CRUD app done in 1 day, maybe something like Ruby On Rails would be the way to go (I know Rails is a framework and Ruby is the language, but these days what libraries and frameworks are available factor greatly into picking a language)