The sound isn't working

If the sound in the videos is working, but the sound of the app itself (background music, interface sound effects, etc) is not, then you likely have your device set to mute. Check the physical mute button (usually located above the volume) and make sure it's not set to mute.

Alternatively, if you can't hear any sound at all, from videos or otherwise, check to make sure your volume setting isn't turned all the way down.

If those solutions don't work, you can try this:

Go to Settings > General > Use Side Switch to > set to Mute
Toggle the side switch button (small plastic button next to volume control) to the right. A red dot will show on the button. The mute symbol (headphone with a slash through it) will appear briefly.
Make sure the audio level is turned up using the volume control button. Mute has been toggled OFF. Now you can switch the side switch to Rotation Lock or to Mute if you like. When you open the app again, the sound should be playing just fine!