The Raspberry Pi has up to three audio output modes: HDMI 1 and 2, if present, and a headphone jack. You can switch between these modes at any time.
If your HDMI monitor or TV has built-in speakers, the audio can be played over the HDMI cable, but you can switch it to a set of headphones or other speakers plugged into the headphone jack. If your display claims to have speakers, sound is output via HDMI by default; if not, it is output via the headphone jack. This may not be the desired output setup, or the auto-detection is inaccurate, in which case you can manually switch the output.
There are two ways of setting the audio output.
Right-clicking the volume icon on the desktop taskbar brings up the audio output selector; this allows you to select between the internal audio outputs. It also allows you to select any external audio devices, such as USB sound cards and Bluetooth audio devices. A green tick is shown against the currently selected audio output device — simply left-click the desired output in the pop-up menu to change this. The volume control and mute operate on the currently selected device.
Open up raspi-config by entering the following into the command line:
sudo raspi-config
This will open the configuration screen:
Select System Options (Currently option 1, but yours may be different) and press Enter.
Now select the Option named, Audio (Currently option S2, but yours may be different) and press Enter:
Select your required mode, press Enter and press the right arrow key to exit the options list, then select Finish to exit the configuration tool.
After you have finished modifying your audio settings, you need to restart your Raspberry Pi in order for your changes to take effect.
In some rare cases, it is necessary to edit config.txt to force HDMI mode (as opposed to DVI mode, which does not send sound). You can do this by editing /boot/config.txt and setting hdmi_drive=2, then rebooting for the change to take effect.