The term "rightist" is not used as much as the term "leftist," but it can be used to refer to someone who holds a rather conservative political point of view.
The definition of a rightist will vary to some degree from country to country. However, a rightist will generally support free market capitalism. They will often be opposed to government welfare programs but will support government efforts to require people to behave in ways that are in accord with traditional values. Rightists will be very anti-communist and will typically support the idea of having a strong military. They will sometimes be quite nationalistic.
In short, these are people who are more to the right of the spectrum of political ideologies.