Isn't it just an un-amplified device in an un-amplified input though? Kinda like putting a record player in anything but the Phono?
It's not quite that simple.
Here's the simplest way (and slightly incorrect, but it sorta gets the job done) to understand impedance matching.
Imagine you have two 600 ohm resistors and a voltage source, both resistors are the same value so the voltage is spread between them evenly. This is sorta what happens when you connect a line level output to a line level input.
Now imagine you have two resistors but one is say 75 ohms and the other is 600 ohms. Most of that voltage source is going to hang around the 75 ohm resistor and only a little bit of that voltage is going to hit the 600 ohm resistor. That's what happens when you plug a headphone level device into a line level device.
Keep in mind that using simple resistive circuits to describe a reactive circuit is a bit incorrect because you're dealing with Impedance not Resistance. So the analogy isn't perfect, but it does the job.