Open your Spotify app and navigate to settings. On iOS, you do this by going to Your Library > Gear Icon > 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.
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: