Research shows that writing by hand has neurological benefits. One paper (Muller and Oppenheimer, 2014) covered three studies of adult learners which led them to the conclusion that taking notes by hand requires notetakers to process information more deeply than those who take notes on their laptops. What happens is that typing notes during a lecture ends up being more like transcription rather than learning. They proved this by asking each set of notetakers conceptual questions about the material for which they were taking notes. Guess who performed better? Right, the ones who took their notes by writing them down.
Another study (James and Englehardt, 2012) found that five year olds were better able to recognize letters if they wrote them down by hand instead of typing them. Because the handwriters were better able to recognize letters, it follows that they're better able to read later on.
A new study on Chinese calligraphy (Chen, He, et al, 2017) reports initial findings that practitioners with at least 5 years of experience in Chinese calligraphy performed better than those with only one month of experience when it came to the executive functions of working memory and inhibitory control. Additionally, the researchers imaged the brains of the study participants using fMRI to see which areas of the brain are affected. In doing so, they were able to discover that those who were more experienced in Chinese calligraphy produced stronger signals in the brain areas which involved working memory.
The important takeaway is that somehow the brain is more affected in a positive direction by the physical act of writing. If you'd like to experience these benefits, try putting away the keyboard and picking up a pen.