First let's consider the question "What's so revolutionary about Bernie Sanders"?
Sanders has political positions which are unusually social-democratic for American politics. When you compare the United States with European countries, the US policies were always favoring a smaller state and a more capitalist system with fewer transfer payments and fewer policies actively supporting class mobility.
Sanders is the first US politician who gained enough support through social-democratic policies to almost become a presidential candidate.
Now "why is this influential"? He lost the nomination, after all.
Because it showed that there is a considerable amount of voters in the United States which favors more socialist policies. Any politician now knows that they might be able to tap into this voters potential by changing their stance on certain issues. The future will show how this will affect the general political course of the United States in the next decade.
Regarding the question "Are people implying the Bernie Sanders movement will result in a violent revolution trying to overthrow the government"?
I believe that most people who use the term "political revolution" in that context do not actually want to imply that. The term "Revolution" is used quite inflationary in the English-speaking world in the past decades (note that when advertising speaks about "revolutionary" new products which will "revolutionize" the market, they are rarely talking about molotov cocktails). Its meaning became a lot softer. Most people who use the term are talking about a considerable change in direction, but do not necessarily imply that this will happen through a violent uprising.