The Department of State was the first cabinet position formed by the new government under Washington. You can go to wiki to find out about the history of the department, but the important thing I would focus on is the fact that it was the first department.
Coming out of the revolution and forming a new country one of the most important things that the United States needed was international relations with other countries. From those relationships you gain allies and trade. Going all the way to the initial problems of the colonies, the colonists were not given fair representation to the royal court, and when the colonists and the colonial governments would send "ministers" to the King to be heard, they were not treated as we would treat an ambassador. It resulted in our new nation not having a backbone of diplomats that could work with foreign leaders and their governments.
Frankly, we only had four - John Adams, Benjamin Franklin, Thomas Jefferson and John Jay.
The State Department started with a ton of domestic powers simply because the new government was forming, but over the years it has become the central administrative and diplomatic arm of the executive branch for foreign relations. The Secretary of State is one of the most important jobs in our government for those and other obvious reasons. It's made all the more clear by the order of succession to the office of President which goes from the President, to the Vice President, to the Speaker of the House (the people's most direct representative as leader of the popular branch) to the Senate pro tempore President ( the stand in for the Vice President in leading the Senate and as a result the next most powerful leader of the people through the legislative branch) and then the Secretary of State.
It's an important distinction. If we assume that there a massive catastrophe that required us to get to the SecState (war, cylons, etc.) then our leader would be the one that all other countries interacted with, whose leaders had some kind of relationship and who would be in the best position to project American leadership to the world in the midst of chaos. To be fair, it's also first among cabinet positions because it was the first cabinet position, but it was first because it had to be. America needed to be seen as a viable country on the world stage.
On a daily basis, most voters probably don't give this office the respect it deserves or the full appreciate for the power and prestige that it has. We seem to think that our President is our chief diplomat and he/she will just talk with world leaders and that the SecState is little more than a bench coach for foreign affairs. But that isn't correct. Far too few people vote for President with an eye on who could be the SecState in that process. The easiest and best way for the United States to project power to the world is to have an effective SecState. That is who deals with foreign governments on a daily basis. And while our system has a Vice President, in terms of effective exercise of power, the SecState is probably the second most important executive branch officer, after the President.