I ran into this issue earlier this year and was worried that the connector on what was still a new laptop was already damaged (without it even having had much use since most of the time the built-in speakers were used). It happened again today; I was curious about others experiencing it, and was surprised to find that while plenty of people seem to have experienced it, but good answers were few and far between.
Fortunately, it turned out not to be a problem.
Most laptops have audio-adapters with auto-sensing jacks. That means that they can detect when headphones are plugged in and can then relay that to the software which can perform different actions such as cutting the sound to the internal speakers.
This issue is most common on laptops that have only a single built-in speaker as opposed to those with two. What happens is that the system, having only a single speaker, runs in mono mode so that the left and right channels can be combined and played through the single speaker.
When you plug earphones into the laptop, you continue to hear the audio in mono mode, and thus only through a single channel. What you need to do is to switch to stereo mode. Fortunately this tends to be extremely easy to do.
The fastest way to switch a mono laptop to stereo mode when using headphones is simply to adjust the master volume level. You can do this through software (e.g., the Windows volume mixer) or through your laptop’s audio hotkeys if it has them (e.g., Fn+⇧). Just make sure that you actually change the audio. For example, if the volume is already at the maximum, then pressing the Volume Up key won’t have an effect, so press Volume Down to make an actual change in volume.
The laptop should immediately switch to stereo mode and the audio should come through both sides of the headphones.
Conversely, you should also adjust the volume when pulling the plug out to switch the laptop back into mono mode because while you may not even notice it most of the time, you may be missing some audio from having only one side being played through the single internal speaker.
(The software can and should be designed to automatically switch modes when it switches output devices, so check if there is a driver update available since it may address this issue.)