When you are listening to music or watching a video on your phone, a Media Player is displayed on your watch to help you control the media playing.

Start by playing a song or video on your phone. A player opens on your watch that lets you play or pause your stream, change tracks and adjust the volume.
If you want to navigate on your watch while listening to music, you can minimize the player by swiping it to the right.
To open it again, return to the Quick Settings by swiping down from your watch face; you will find a small playback bar below the other shortcuts. Tap it to expand the player and access full commands. If the player goes to sleep, simply touch the screen to reactivate it.
The music controller disappears on its own when you close the media player on your phone.

In case your want to turn off or to turn on the automatic launch of the controller, do a long-press on the player when launched and disable the ‘Autolaunch media controls’.

Some third party apps can offer to listen music offline, for these ones you would require to have a premium subscription. To do so, you would need to be connected to your headphones on your watch, follow the steps in the article in order to pair your device : https://support.google.com/wearos/answer/6345084?hl=