I just started my first semester of college and I'm going to be a history major. I really gotten into the habit of listening to podcast recently while I'm doing other things so I kind a like to get ahead on my studies and I also just fine history very interesting. Can someone please recommend some good podcasts that discussed history to some degree?
Good US history would be the Journal of American History Podcast. The podcast is produced by the Organization of American Historians, one of the two major associations of historians in the United States (the other being the American Historical Association). Unfortunately, it stopped updating sometime around 2016 (I am unsure when or if it will resume; I've been meaning to email them). The exact topic of the podcast will vary. Many will discuss articles that previously appeared in the journal, so if you prefer a sort of back and forth approach or like listening to things over reading them, etc., the podcast might be helpful. I do not think there have been too many roundtable sort of discussions, which is unfortunate.
If by World History, you mean not-Europe, not-US, I would suggest Ottoman History Podcast. It is not a generic world history podcast (e.g. it doesn't deal with the whole world), but focuses specifically on the Ottoman Empire throughout history, which does mean it can hit on Islamic History, African history, Balkan history, etc. My personal favorite section is their History of Science playlist (found here http://www.ottomanhistorypodcast.com/p/blog-page_18.html) because I rarely do History of Science. They also have playlists dedicated to gender in the Ottoman world, law in the Ottoman World, etc. The basic structure is normally an interviewer interviewing either a phd candidate or full-fledged phd about their field of interest, with a fair amount of background given for lay viewers. I've also noticed that many of the people interviewed seem fairly young, so it is normally easy to find their dissertations and therefore to find out more about their research. Each episode comes with it's own bibliography.
The website itself also has a number of cool documents with introductions describing them. My favorite has is the one about the Ottomans discussing Mormanism and whether the ban on polygamy was anti-Muslim or not, unfortunately as far as I can tell, they just give a summary of the document rather than a translation (http://www.docblog.ottomanhistorypodcast.com/2015/01/ottomans-discuss-mormons.html?q=mormon).
Have you given our own /r/AskHistorians Podcast a listen!? If not, there is a nice back catalog to take up some of your time.