It's all to do with 'Monitor Calibration'. Imagine you have a photo on your screen and you print it and it looks OK. Now reduce the brightness of your monitor to the lowest setting so the screen is almost black - you'd expect the photo to print in the same way as it did before, wouldn't you? Similarly if you set the monitor to super-bright, reduce the colour of the monitor so the image looked black-and-white or super lurid colours. You wouldn't expect any of these monitor adjustments to affect the way the photo printed, would you?
So if you are editing a photo onscreen and very carefully editing (in Lightroom etc) the shadows and highlights to just the way you want, and if adjusting the monitor brightness up and down completely ruins how the photo looks, how do you know exactly how it's going to print?
The solution is a 'Colour managed workflow'. This attempts to ensure that what you see on screen will match pretty closely to what you get on paper. It involves calibration of the screen and your printer (if you print at home), preferably with hardware calibration tools.
The monitor calibration adjusts the colour of the monitor (because when the computer tells the monitor to display a pixel as pure red, what is actually displayed might look a bit yellow for example, due to the glass, hardware in the monitor etc. Hardware monitor calibration will create an ICC profile for your particular graphics card/monitor combination to correct this). It also sets brightness, contrast and greyscale to standard values.
Printer calibration does a similar job - you print a colour target (a grid of colour) and then measure it with a device (photo spectrometer - basically a specialised scanner) that knows what colours were supposed to be printed and can measure what colours were actually printed. It can produce a colour profile that will be unique for the printer, ink and paper combination used (yes, you'd need a different profile for every different paper you use). Some paper manufacturers have profiles for their papers you can download, which is a good compromise. You then specify the printer profile to use when you print the picture. The profile effectively tells the printer driver that when trying to print red, add a bit of yellow (for example) to compensate for inaccuracies in the way the printer tries to make red, or how the paper absorbs the ink or because the inks aren't quite the right colour etc.
This is the 'proper' way to do it and it can get expensive, but results can be very satisfying, as you can edit a photo to look just the way you like and know that when you print it, the print should match what you saw on screen.
It's possible to calibrate you monitor using software which is a good compromise: try this help page to perform a software calibration of your monitor: https://helpx.adobe.com/lightroom/help/color-management.html.
You calibrate your monitor (using hardware or software) in specific lighting conditions (e.g. lights on, lights off, curtains open, closed etc) and you should do final editing under those same lighting conditions. You also mustn't adjust the monitor (brightness etc) after calibrating.
For printer calibration, if you don't do your own printing you don't have to do this. The print company you use should have colour-managed printers.
For your particular example, it sounds as though your monitor is too bright. Try doing a software calibration on it.
Try to have the room in shadow (complete darkness isn't required) - a brightly lit room is problematic. Sunlight directly on the screen is a big no-no.
Once your monitor is calibrated, it will be interesting to see if the photo on screen matches the print you got
