Right refers to conservatism. Left refers to liberalism. Red state refers to conservative-leaning states. Blue state refers to liberal-leaning states. I hope this helps.
In the US for the last 150 years the two leading political parties have been the democrats represented by the color blue and the republicans represented by red. Blue states are therefore predominantly democrat and red ones predominantly republican. Originally the republicans championed more left wing progressive politics that advocated change, while the democrats were the more conservative right wing party that resisted change and promoted traditional values. Today the situation is reversed with the republican party advocating traditional values and resisting change and the democrats championing moving forward.
Primary elections are how the two parties choose candidates they wish to run for office.
Politics is the art of getting everyone else to do what you want because you've convinced them to see it your way.
Far Right wing is either Libertarian or Authoritarian, or Individualist and Fascist in rough terms. Far Left wing is either Anarchistic or Communal, or Collectivist and Communist. For everyone that doesn't operate on the extremes they would define themselves inbetween these two extremes. Which would be Liberal or Conservative depending on their view point. So that's Democrats, socialists, anarchists, communists, and centrists (fiscal conservatives) on the left. Republicans, libertarians, Fascists, Nationalists, and centrists (social conservatives) on the right.
Red state means solidly republican/right wing. Blue means solidly democratic/left wing. Primaries are not only colors. They are a process through which the states choose the candidate that by majority rule represents them. After the primary process the winner emerges and campaigns against the Incumbent President. After the votes have been tallied the candidate with the most votes electorally and popularly, is sworn in on January 20th as the president.
Kudzu41999 explained it very well but the depth of it all can be complicated with a lot of in between such as "moderate." I strongly encourage you to keep on until you learn as much as you can about politics but don't depend on finding truth from the media. Dig deep and even to the point of studying some history. Read about both Left and Right and decide for yourself and only for yourself where you will lean. Never ever feel like your vote doesn't matter!!!