I’m coming from a computing background and trying to learn about circuits, but having trouble with this terminology because it the opposite of the norm in computing (where nodes are connected by branches).
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It’s to do with the measurements that can be taken. And I’m going to talk completely ideally here. Like year 1 circuits class where all wires have 0 resistance. V=IR, the voltage drop across a thing is the current running through it times its resistance. No resistance means no voltage drop across the wire. So if you take your voltmeter and put one probe at ground and the other on some wire connection, you’ll get some voltage readout. That exact same voltage will be read no matter which side of that wire you probe. Or if there are several wires joined together, anywhere in that node. That also means any component connected to that node will see the same potential value on whichever leg touches that node.
Keep the image of several wires connected together. Say, a battery feeding to 7 LEDs (maybe a 7-segment display). It doesn’t matter how many of the LEDs are connected, the voltage will stay the same. And the current through the diode depends entirely on the voltage drop across it, so each diode receives the same current. Imagine then, that there are 7 LEDs on, each drawing 10mA of current. That means the battery must be supplying 70mA which enters the node, and then ‘branches’ to each of the LEDs. Furthermore, the sum of currents entering a node must equal the sum of currents leaving the node. So if you put two components in series, they must have the same current. If you put an ammeter at any point in that branch, you will read the same current.
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