The Council approves all candidates for election to the Iranian Presidency, legislative branch, and the Assembly of Experts.
Six members of the Council are clerics selected by the Supreme Leader, who serves as Iran's Head of State. The other six members are lawyers proposed by Iran's head of judicial branch (selected in turn by the Supreme Leader), and voted in by the Parliment. Members are elected for six years on a phased basis, so that half the membership changes every three years.
As mentioned, the council also holds veto power over all legislation approved by the Majlis. It can drop a law based on two accounts: being against Islamic laws, or being against the constitution. While all the members vote on the laws being compatible with the constitution, only the six clerics vote on them being compatible with Islam.
If any law is rejected, they will be passed back to the Majlis for correction. If the Majlis and the Council of Guardians couldn't decide on a case, it is passed up to the Expediency Council for a final decision.