A great review of this subject comes from a really interesting article at PBS. Take a look at this excerpt:

In what’s thought of as a traditional primary, political candidates only compete against other contenders within their own parties for nominations, to then advance to the general election. States hold their primaries on a variety of dates, with winners competing with one another on the November ballot.

But in a “jungle primary” or “majority vote primary,” all candidates regardless of party run against each other on the same ballot. If no one candidate tops 50% in that primary, the top two vote-getters advance to a head-to-head runoff, which can end up pitting two Republicans or two Democrats against each other.

Read the full article here. Also, see related Democracy Chronicles articles like those on the Voter Access, Voter Turnout, or even seen our section on American Democracy.