Graphic design in a broad term involves working with text and images. If you want to be good at it, it's essential that you have an understanding of the underlying principles of typography, illustration, photography and web technology if designing for web.
When I was in university doing my design degree, I basically learned the essentials mentioned above but there is one thing that I feel I should have paid attention to. And, that is TYPOGRAPHY. I learned the basics of calligraphy and typography took a big part in the course but I guess I didn't invest in myself enough time practicing what I learned. If I realised earlier how much impact it would have on my future work, it would have been a different story.
Whether you design for web or print, it's all about delivering a clear message and communicate through words. Take a look at software for example, about 90% a user interface is consisted of words. It requires a strong sense of typography to be able to set a clear visual hierarchy using just words.
Say, you're a logo designer, most of the work will involve experimenting with a typeface. To be able to experiment with it, there are certain rules around typeface you will need to know, such as horizontal strokes are generally thinner than vertical strokes or "O" should go slightly over the baseline and more. You still can create your custom-shaped letters without knowing all these but I can guarantee that it won't be satisfying outcome at least for your client. There are so many details hidden in the letters unless you look very closely and there are certain parts of letter shape you want to retain to look like a proper letter shape.
I'm revisiting my handwriting style using various tools at the moment. Not to switch my design field from digital to analogue or to impress some one with my handwriting, but to solidify my understanding on good typography so I can make a better decision with my work. I also believe that in this overly saturated digital space composed with stock images, default icon style and computer based typefaces, a unique handwriting with a personal flair has a potential to set you apart from the rest.