Find the Streaming Quality settings pane
Open your Spotify app and navigate to settings. On iOS, you do this by going to Your Library > Gear Icon > Streaming Quality.
Increase Spotify streaming quality
You'll see several options, with Automatic selected by default:
Automatic (Recommended) Normal High Extreme
Below is the streaming quality associated with each option:
Automatic (Recommended) - varies between Normal and High Normal - 96kbps High - 160kbps Extreme - 320kbps
What is Spotify's Automatic streaming quality option?
"Automatic" toggles between Normal (96kbps) and High (160kbps) depending on the quality of your cellular reception. However, it never uses Extreme.
Since I listen to Spotify on WiFi most of the time and have a pretty ample data plan, I've selected the Extreme option.
Note: Extreme quality is only available to Spotify Premium members
However, all members have access to High, which is still pretty great.
How much of a difference does it make?
Audio streaming quality is measured by bitrate (in kilobits per second, or kbps). This is the amount of audio data transferred per second so, naturally, a higher kbps results in higher quality music reaching your ears every second. Changing this setting from Automatic (96/160kbps) to Extreme (320kbps) increases your Spotify audio quality by up to 3X.
This YouTube video does a good job of illustrating the range of audio quality up to 320kbps: