Empirical evidence (also empirical data, sense experience, empirical knowledge, or the a posteriori) is a source of knowledge acquired by means of observation or experimentation. The term comes from the Greek word for experience... Notice there is nothing in there about counting and using math. There are folks in my school who do this, but it is not their fault--they are economists (we cannot hold such folks responsible for their social skills [just teasing]). In political science, this still happens, and mostly because of old habits, I think.
There is work in political science that is not empirical: game theory, formal modeling, political theory. But most of the work published is empirical in one way or another. Similarly, some folks will use the word systematic as if to suggest all quantitative work is systematic and all non-quant is not. Believe me, as I have reviewed much quant stuff (and written some), not all of it is that systematic. And much work using comparative case studies is quite systematic and some not. Systematic is a variable, not a constant, for any method. Same goes for rigorous (thanks to @alb202) for reminding me of that one.
This is, of course, mostly a debate for grad students, as mature political scientists realize that each method has strengths and weaknesses, and that the best work often involves mixing methods. Indeed, the one trend I noticed over the past ten years or so of the job market is that many of the most successful candidates are those that use multiple methods.
My career path has crossed the supposed quant/qual barrier, as my early work was entirely qualitative (comparative case studies) and then I found a handy dataset for asking a variety of questions, producing some of my most cited work, and then I found myself doing more qualitative work as I interviewed military officers, government officials and others about their country's Afghanistan operations. My current projects, as I ramp up the next big qualitative project, include a bunch of different quant projects of varying degrees of complexity (the heavy lifting of the quant techniques is being done by younger, savvier co-authors).
Maybe I am too dismissive, perhaps the quant/qual wars are taking place somewhere outside of the PSR threads. There are probably departments where the fight still resonates quite a bit. From my vantage point, where I see glimpses of the job market, and where jobs are the most precious resource in our business, the mixed methods folks doing so well is very suggestive to me. It is certainly the case that journals have certain tendencies (that the very scarce resource that is an APSR article is still distributed in a particular way). The good news is that the quant and qual people can join together in being threatened by the experiment zealots.... or they could until a few weeks ago.
All I know is that when I hear empirical, it makes me think of the key move the Realists made in IR, as they try to define everything as as Idealist. There are lots of names in this game, and lots of gaming of names. Which means I can invoke Omar.