What do solid/striped lines on a wire indicate?
The solid/dashed lines on wires like the ones pictured in your question are used to indicate polarity e.g. for the "wall wart" power supplies. Usually* the wire with the white stripe or the dashed lines carries the "positive" (+) end, while the other, unmarked wire carries the "negative" (-) end.
It doesn't matter if it is striped or dashed, the presence of any kind of marker is the indicator of the wire being the "positive" end of things, as opposed to the unmarked "negative" wire.
This kind of convention is used on speaker cables as well, where the wire that is marked in some manner (e.g. text providing wire information, a stripe, etc.) is the positive end, and the unmarked wire is the negative end.
*I say "usually" since I've seen a wall wart with the wires were reversed, although every other wall wart I've used does it the way I've described above. The only way to be sure is to use a voltmeter and measure the voltage across the two wires. If you get a negative voltage reading, you know you have the test leads swapped.
What about electrolytic capacitors where the white stripe signals the _negative_ pin? At first I got confused by the wire convention being the opposite...
Less expensive speaker wire, often called zip-cord, indicates polarity with a raised ridge on the outside edge of one of the conductors rather than striping. You frequently find that convention on wall-wart wiring, too.
Twisted pair used in network cables and some phone wiring indicates pairs and polarity with a similar scheme. Each pair has a different base color, such as blue, green, or orange. The polarity is indicated by having one wire a solid color and the other with a white stripe on a background of the same color.