What do people mean when they say "Notice me, senpai"? I'm new to anime and my friends really like it. They really like to say to me "notice me, senpai!" and I don't get the reference. I could be walking to class and one of my friends would say "Can you go to the canteen?" and I would say no I can't and then, they will say "NOTICE ME, SENPAI!" Can anyone shed some light on the "notice me, senpai" reference, please?
This is a meme in the English-speaking internet anime community. This particular phrasing appears to have come into existence around December 2013 (according to Google Trends), though variants are known to date back to 2012.

It does not directly reference any particular work of anime or manga. Rather, it is inspired by a reasonably common trope of anime/manga writing about school-age children, whereby a character (usually a girl) will have a personal or romantic interest in an older student at their same school (which is what a "senpai" is in this context), but instead of doing a dag-blasted thing about it, just silently hopes that the senpai will pay attention to them. This narrative trope is particularly common in shoujo media.

Goodness knows why your friends are exuding memes in real life; you would do better to ask them about that. As a meme originalist, I cannot help but notice that the contexts in which your friends are reportedly using this meme don't make much sense.