Someone who's dovish favors political policies that promote peace, rather than conflict with other countries. A dovish president is more likely to sign peace treaties than to start a war.
While dovish can mean simply "peaceful and innocent," it's much more common to find it in political writing or speech, particularly in contrast to hawkish. Dovish advisors and cabinet members can influence a government to strive for peaceful resolutions to conflict, while hawkish politicians tend to favor aggressive policies. This political meaning dates from the 1960s.