Magsafe 2 Troubles

Try unplugging your power adapter from the electrical outlet for a minute so it can reset the electronics inside it. Sometimes the power adapter can get into a weird state. Also try another electrical outlet in case the one you are using has a problem.

Also check out this Apple article to check your power adapter and the magsafe port on the laptop.

https://support.apple.com/en-us/HT203207

Option click the battery icon on the menu bar and check the battery condition. If it shows anything but "Normal" or "Good", then the battery may need replaced.

Try running the Apple Diagnostics.

If these things don't help, then you may want to take your laptop and the power adapter to an Apple Store to be examined to determine if all you need is a new power adapter or if there might be an issue with the laptop.

If yours is the L-shaped computer-end, these sometimes develop a problem.

If you can rotate the L-shaped bit more than a few degrees axially (relative to the center of the cord) it may have an internal short in the L-shaped adapter-end. This can cause exactly the symptoms you describe.

A correctly-working unit should be rigidly fixed on the cord, and will not rotate more than a few degrees.

The T-shaped ones can also develop a similar problem, but it is less likely.

@Grant's advice reminds me that some times the laptop side case can be just slightly deformed making the L shaped Magsafe not seat properly. Sometimes the Magsafe just needs to be wiggled and repositioned on the Magsafe connector. Also check for something stuck on the Magsafe port of the laptop since it tends to attract staples and other metal fragments.

Grant Bennet-Alder wrote:

If yours is the L-shaped computer-end, these sometimes develop a problem.

FYI, I just realized the title mentions Magsafe 2. I think Apple only made the "T" style with Magsafe 2.

If your Mac battery won’t charge - Apple Support