A civil war is a division of a nation that results in two factions competing internally for control of a country, often the current government and coup-d'etat forces with a claim on rulership, or sometimes the govt collapses and two groups both attempt to seize power. You get the idea - internal strife and claim to the nation (or sometimes to just part of a nation that the other considers inseparable).

A proxy war - which can cause or make use of a civil war - is a war between two countries who both remain removed from the direct conflict, but playing benefactor to each side because they support opposing outcomes. For example, after the Nicaraguan Revolution was a civil war between the new socialist Sandinista government and the collective of right-wing and independent groups known as the Contras - the USSR happily supported and supplied the Sandinistas, while the Reagan administration of the USA backed the Contras. Thus, the Nicaraguan Contra War became a proxy war for the USSR and USA - extremely common during the Cold War.