Your mother is right. Blinking is the rapid closing and opening of the eyelid. It is an essential function to spread tears across and remove irritants from the surface of the cornea and conjunctiva. If you open eyes in a long time, you can easily get dryness, sore and pain in eyes. Sometimes irritation and eye infection may occur during your constantly opening. So do not open your eyes in a long time and blinking eyes often to keep eye health. Plus, work with computer, stare digital screen in a long time also can reduce uncomfortable by blinking.
Yes, blinking your eyes has great function, moisture your eyes and getting rid of the outside dust. If you keep your eyes open for a long time with no blinking, your eyes may get infection because of the coming invisible bacterium. You could also be dry at the eyes which will make you feel uncomfortable at the eyes. You should not do this on purpose. It is so bad for your eyes.
As your mother said that often blink eyes can keep eyes moist. This is very important for our eyes because if your eyes open for a long time, it will be dry, painful and tears. Even if you will get some of dust and bacteria on your conjunctiva. Anyway, it's not good for your eyes.