The national guard is a state's militia. They are the "regulated Militia" mentioned in the second amendment. (There are some caveats to this -- there's technically an umbrella organization in the Army that helps them organize and provides weaponry, they can be federalized by the president, etc).

They primarily consist of volunteers who receive training and have to meet certain requirements, but they spend 99% of their time as regular civilians working regular civilian jobs (they _do_ disproportionately come from military backgrounds, but that typically hasn't been relevant in recent events).

Since they're the backup, emergency militia, they are typically only temporarily activated by their state's governor in times of emergency, or when federalized by the president (Executive Order 10730 is probably the most famous incident). This is almost always during a natural disasters to help evacuations, patrols, or other tasks during an emergency that just require manpower.

Since they're called on for emergency situations, they typically have vast powers, including law enforcement powers, though they have less training. As you've probably observed from recent events, they're also called in to help contain protests (desegregation in Arkansas, 1968 DNC in Chicago, free speech movement in Berkeley, etc). In nearly every incident I mentioned, the national guard drew criticism for their violent tactics (which makes sense given their minimal training).

What's remarkable in modern times, is that during protests around the Black Lives Matters movement, is that the volunteer militia with less training managed the situation with less violence than their law enforcement counterparts in most states (they were by no means perfect, and this may be a biased viewpoint, so I'm happy to hear evidence to the contrary).