What a space navy does

RogerBW

Expeditionary/Force Projection

(to be expanded)

System/Planetary Defence

Antimatter

Even commercial ships need a fair amount of antimatter, and this has to come from somewhere. It is created at solar-powered factories, then shipped to where it’s needed.
These factories and ships are obviously tempting targets for pirates, terrorists, and state-level enemies. It’s always possible to blow up an antimatter facility and thus deny it to everyone, but everybody would prefer that that didn’t have to happen.
In most systems the factories are close to the sun. Space traffic control will be aware of unauthorised ships nearby (there’s little navigational reason to get that close, and factories have large areas of controlled space around them), and if there are enough system defence craft one is likely to be nearby. Antimatter freighters are allocated courses outside usual traffic patterns, and again unauthorised ships will be warned off.
Pirates attempting to obtain antimatter will usually try for the freighter, hoping to get aboard, retrieve the material, and force the jump point before defences can be organised. It’s a very risky business, and usually they rely on draining fuel from captured ships.
A terrorist group needs very little antimatter, and will typically try to obtain it by infiltrating someone into the production or transport crew.
A state actor invading the system will hope to capture, but will be resigned to destroying, the production plant. (Sometimes a crew can be persuaded not to set off the failsafes, especially if they think the system will change hands again soon.)
In some systems, particularly in frontier areas, a production plant is placed near the jump point; this vastly reduces the antimatter production rate, but it saves on freight costs and delays, and it can share any static defences the jump point has.

Anti-Piracy

The jump point setup means that, quite a bit of the time, a ship moving long distances will travel through several uninhabited systems while getting from civilised world A to civilised world B. That is where pirates can strike.
Pirates can’t afford to run huge freighters themselves, so what they’ll be doing is not so much looting the cargo as taking the whole ship. They’ll pick a system with at least three jump points in it, capture the freighter by threats and boarding (basic civilian anti-meteor lasers won’t deter even a lightly-armoured old warship), and take it elsewhere.
How do they make their money? By scrubbing off identifying marks on the cargo and indeed the freighter, and selling them somewhere people aren’t too discerning which isn’t part of the colonial holdings of the power that owned the freighter.
A naval escort will absolutely prevent piracy, because the pirates know they can’t win against it: they’ll just hide and wait for an unescorted ship to show up later. And sending naval escorts feels more expensive to the government than missing some targets feels to the pirates. There may be Q-ships, or naval forces lurking just the other side of a jump point, hoping to catch up with a captured ship before it can be got out of the system…

Transportation

(to be expanded)

Long-Range Exploration

This is the Deep Survey branch; (to be expanded).

Boarding/Landing Operations Support

(to be expanded)

Naval Gunfire Support

Orbital fire support is often a decisive factor in planetary engagements from colonial scuffles to all-out war, but it’s a tricky business. The Naval Gunfire Liaison Officer needs to serve as the link between ground and orbit, juggling an often fluid battle situation, an up-to-date picture of the predicted delays between firing and strike, and the positions and orbits of firing ships. (This latter is why the Navy prefers to use its own people for the job.)
The NGLO is placed on the ground usually with the Royal Marines but in some cases with regular Army units; he’s typically placed in an artillery command centre but is trained to act as a spotter.
Orbital laser fire is functionally instantaneous, but requires the ship to be above the horizon. Particle beams are rarely used, because the neutral beams favoured for space engagements tend to decohere when they hit atmosphere (though on airless worlds they can still be of some help). Missiles are typically delayed by about five minutes, up to twenty if the ship is on the far side of the planet when it fires.