Thank you SO much, everyone who helped. I now have to work out what "power flags" are, and how to attach them to things; this is all a new language to me, replete with a whole new set of words and systems.
First: a "net" is the term for a connection between two or more pins.
A "Power Flag" is Kicad's mechanism to fix an issue that comes up in Electrical Rules Checks. (ERC is in schematics, Design Rule Checks or DRC are in PCB.)
The pins on schematic symbols can have electrical types, like Input, Output, Open Collector, and so forth. For power connections there are Power In pins and Power Out pins. Most of your ICs have power pins, and those get a Power In type.
Any pin that's a Power In must be driven by one (and only one ...) Power Out pin. After all, the goal is to provide an admittedly primitive way of checking connections: all power pins have to have a power source, right?
When you place a Power Symbol (like +3V3 or +5VA or the like) from the Power library, you add a global net (same net on all sheets in the design) with that net name (+3V3, +5VA, whatever) to the schematic, and you connect that net to the pins on which you place that symbol.
Here's the rub, though, and it's somewhat non-obvious. The Power symbols are a one-pin symbol, and that pin is declared as a Power In type. It is
not a power source. This makes sense, when you think about it: all the power symbol does is to declare a global net. It does not "drive."
The output pin of an LM317 regulator is a Power Out pin. When you connect that pin to a Power symbol, you have satisfied the ERC requirement that all Power In pins on that net must have a driver.
But what if your board doesn't have a regulator, and instead you have a connector through which you get your supply voltage. Say you get your supply from a board-to-board connector, or a Phoenix connector with pins, or whatever. Connectors are usually designed with their pins designated as Passive, because you don't know how they'll be used from one design to the next. So you place your connector on your board, connect a Power symbol (+3V3, etc) to the pins you designate for supply voltage, and you run ERC. And it fails because there is still no Power Out pin driving the power net.
This is where the Power Flag comes in. A Power Flag is a one-pin symbol and that one pin has a type Power Out. (Like a Power symbol, it has no footprint and doesn't appear on the BOM.) When you place a Power Flag on the undriven supply net, the Power Flag provides that driver. Run ERC and it will be happy because now your +3V3 net has a Power Out pin driving it.
Other uses for Power Flags include:
1. Say you have an AC mains plug connected to a transformer, and the transformer drives a diode bridge, and the diode bridge drives your LM317's input pin. That pin is a Power Input. A diode's pins are of type Passive. So while you "know" the LM317 has a power input, the ERC doesn't know that. Place a Power Flag on the net that connects the bridge output to the 317 input, and now the 317 has a proper Power Out driving it. ERC is happy.
2. Say you have a switching regulator with post filtering, and you connect that filter output to your +3V3 rail by placing a Power symbol on it. Now you have a global net with name +3V3 and that's connected to all of your logic chips' voltage supply pins. The filter components have Passive pins, so ERC thinks that all of your logic devices' Power In pins have no driver. Place a Power Flag on the +3V3V rail somewhere and now ERC is satisfied.
Don't forget: ground pins on your ICs and such are designated as Power In also, so your GND net must also connect to a Power Out pin. In the cases described above, you will need to put a Power Flag on that net to satisfy ERC.
Is this a hack workaround? I don't know. I don't care. It is a clever solution to a problem. Of course you could always just not use the ERC feature and Kicad won't care, but why? It's there, use it.