As in ownership and control.
Lawmaking - The Government is that which makes the laws about stuff.
Law enforcement - Enforce the laws that one makes.
Judiciary - Make judgements about the laws one makes.
Infrastructure - These sort of investments are of such a long term nature, very hard to structure into a market, are natural monopolies, have risks which are hard to insure for, have little advantage of competition, and competition can cause unnecessary duplication of infrastructure and waste. eg Roads, Rail, fibre-optic networks, power networks, airports.
Fallback basic primary school education - Government owned and controlled schools can compete on an even keel with private schools at a primary school level.
Fallback basic universal health care - including emergency, preventative and educational. "elective" stuff should be private.
Pensions - same reasons as for infrastructure. Highly regulated private superannuation system as in Australia is great too.
Disaster recovery - As opposed to insurance, there is no reason why any private interest would have a spare reserve trained specialists for immediate help. The Australian army seems much better for instance.
National Security - Command and control is necessary to at least protect the functions of government.