Grid supplies generally come in two flavours,
Single phase means you have 2 wires coming from the street, an active wire, usually red, and a neutral wire, always black.
As an alternating current, it ebbs and flows, changing polarity 50 times every second to give us a 50Hz AC sinusoidal wave
To simplify, in a single phase supply the energy flows in via the active, through your meter and main switch, and onward via RCD/circuit breakers, into the wiring and to your appliances. That same energy returns via the neutral wires to complete the circuit.
(If any of that energy "leaks" out of the system ie because you dropped the toaster in the sink, then the RCD/safety switch will trip off because it sees an imbalance between the active and neutral. The same thing happens to appliances with internal faults, the earth wire, the vertical third pin on a wall socket, carries the leakage safely to ground)
Your solar inverter connects to the same switchboard, and your appliances will use that solar energy in preference to grid energy, so the retail meter only measures what's coming or going to the grid. A customer owned consumption meter is also a good option to be installed at this point, so you have visibility of what's going on.
A 3 phase supply has 4 wires, 3 separate actives and the same neutral that a single phase house does.
The difference is that these three active supplies are staggered from each other, if you imagine the ABC logo where there are three peaks in a wave, not only do you have an up and down potential in terms of alternating current rising and falling, but there is also a potential across the three waves because they're staggered from each other left to right.
What it means is that large loads like a motor in an air conditioner can work very efficiently using the 400 volt potential which ebbs and flows across between the phases.
However small appliances operate just like a single phase house, drawing current from one of the active supplies with a return circuit via the neutral.
In essence everyone has a single phase house, but if you have three supply wires coming from the street you have triple the capacity available, needed for big loads like floor heating and EV charging, plus an added bonus is that things like electric motors operating on 3 phase are inherently more efficient.
What about 2 phase?
That is a little trickier because there's two kinds of "two phase" supply.
Firstly there are some places in towns and suburbs that just have two phases supplied out of the three that are available on the street. Often this was done to put the house loads on one phase and the hot water service on another, each with separate single phase meters.
You can have a single phase solar system but it's best to connect all your typical daytime loads to that phase. You can have two single phase inverters as well but it will probably be best served with a 3 phase consumption meter either way.
The other kind is split phase
Out in the country they often have Single Wire Earth Return supplies strung across long distances. When you have two phase supply from a SWER transformer the AC waves are directly opposite each other, 180° apart means 460 volts rated supply (instead of the 120° stagger of a 400V 3 phase system in the picture above)
Occasionally there were things like milk vat refrigeration or large hot water services which used both phases at 460 volts but generally it would be considered two phases supplying different single phase loads.
SWER connections will need 2 separate consumption meters to give you proper solar monitoring and export control.
Two phases need two separate single phase inverters
Especially on SWER connections where voltage rise becomes an issue that might see your solar throttled on one phase, while the voltage is simultaneously depressed and consumption can still be billed, on the other phase.
There's some extra expanse but that also means you can have more solar, because the network companies limit solar input, normally to 10kW per phase, or 5kW on SWER.
How does this affect solar?
You can have 3 phase supplied to the house and a 3 phase solar inverter will work best because it's inherently balanced.
You can also have one, two or three single phase inverters connected, this often happens when different systems are installed across the years, however the network authorities insist that they should be similar sizes and at worst not more that 5kW different from each other. (3kw in WA)
If your house has two phase 120° supply from the street you can use one or two single phase inverters but may need a three phase consumption meter.
It's quite normal to have a 3 phase house with a single 6.6kW inverter and the retail meter will balance the solar output with grid input to make sure you're not paying to import on two phases and being paid very little to export on the solar phase.