These are terms that have to do with the attitudes that people hold towards wars or military interventions in general (or towards specific cases in which the US is involved militarily in some other country).
The term hawk is used to refer to someone who tends to back military involvement. For example, as you can see in the link below, hawks in the Vietnam War backed expanded American action in that war. They applauded the bombing of North Vietnam, saying that it would scare the Soviet Union.
By contrast, the term dove refers to people who do not want the US to be involved militarily. In the link, the doves feel that the bombing of North Vietnam will backfire by making the Soviets take more of a hard line towards the US.
These terms can be used in reference towards any military involvement by the US or they can be used about people's attitudes towards military action in general.
Politicians, who are inclined towards realist thinking and favour the use of military brinkmanship, threat of force and aggression rather than peaceful negotiations, are often referred to as hawks. In contrast, politicians that prefer negotiation, reconciliation and compromise to direct armed confrontation are referred to as doves.