A minority president is a candidate who is elected without earning the absolute majority of popular votes. There are a few ways in which a presidential candidate may be elected in that way.
One way that a minority president can be elected is if the country is so deeply politically divided that one candidate is not able to achieve the required majority. A minority president could also take office if there was a third candidate that took away enough votes from the other candidates so no one was able to get at least half of the national popular vote. A minority president could also be elected if one candidate secures the popular vote in a few important states, but another is able to take the lead in enough states to win the majority in the Electoral College.