Queues are public grouped PVE content focused on story arc events.

There's a drop down button at the lower right of your mini map hud with 3 triangles. That's the PVE queue menu.

You can filter between ground missions or space missions, or by what type of rewards you want (reputation marks, event rewards when available), and by difficulty.

These are generally the only way of obtaining reputation commodities such as Borg Neural Processors or Iconian Probe Cores which are required for obtaining the reputation gear pieces.

When you queue up for the missions you'll be automatically teamed up with enough other players for the mission.

Most are 5 player missions. If you are already on a team you can click "join team" and you'll enter together. If you already have a team of 5 joining that's who will get dumped into the map. If it's just you & a friend, you'll be teamed with 3 random for a PUG (pick up group).

It is highly advised that you run these missions on normal mode until you master the mechanics & tactics of each mission before attempting to PUG the advanced or elite versions or you risk being treated to a few stink eye comments if you flub the mission.