I see this phrase thrown around a lot, but what exactly does it mean? I've heard the definition of "a nation that can influence other nations", but I get the impression that there is more meaning than that. The second part of my question is what makes a nation a great power? What are the requirements to get this status, basically? For example, what did Sweden do in the 30 years war and Prussia do in the seven years war that gave it the status of great power? Was the term even used to describe a current nation, or is it a historical term?
I was a history and international relations major as an undergrad, and here is where the two disciplines meet. The term "Great Power" comes from the Realist tradition in international relations. Without going too far down the rabbit hole of explaining what Realists believe, they essentially view international politics as a struggle for survival between nation-states and they see power rather than ideology as the key variable that leads nations into conflict (ideology may be an important reason why a war is worth fighting for the common man, but the conflicts are ultimately driven by competition for security between nations rather than conflicts over ideology.)
Realists like John Mearsheimer would define great powers generally as those which have a significant military capability (including latent capability) and an influence on affairs that extends beyond it's immediate region. Great powers can also extend their territorial influence beyond their defined borders in the absence of another power stopping them from doing so. There's not really a hard-and-fast way to differentiate great powers from lesser powers, but a nation that stands a realistic chance of defeating another great power in a war is generally going to be considered a great power.
The term was much more relevant in the absence of superpowers, which are essentially magnified great powers capable of projecting power over vast regions of the globe. Great Powers are much more important when there are powerful states with great military capabilities with no clear hegemon dominating a region. Historically, Western Europe has often been characterized by competition among Great Powers including Russia, England, France, the Netherlands, Germany, and Spain. Certain of these countries have dropped off the list of Great Powers at different points as their ability to influence affairs beyond their boarders lessened and their military capabilities became weakened. Now, some people would characterize Germany, Japan, the UK, France, and Russia as Great Powers (although these are all arguable) but most IR Realists would say that the United States is the sole Superpower in the world, rendering Great Power status fairly useless.