What does it mean or what is the difference between digital and analog electronics? 

This might best be answered in relative terms as to how these two levels of technology have affected consumers. 

For instance, a good example of analog electronics is your VCR used in the early 1980s (40 plus years ago) to watch movies at home. It had buttons to fast forward, play, reverse, record, power on/off etc. These buttons made your VCR work. They did just what they were designed to do when you press them. At the time that they were made, you likely had no expectation that a VCR should do anything more. 

Fast forward to today. 

Digital electronics have arrived. The strongest attribute of digital electronics is the ability to change for improved capability and increased functionality. As an example, think of a modern digital smart phone. It has the means for you to add applications to increase its function in limitless and personally appealing ways --- all to improve your experience and  increase the utility of this wonderful tool. 

Wouldn’t seem logical then that a state-of-the-art quilting machine would have digital capability? 

When shopping for a longarm, it is strongly recommended that you rely on only the brands that feature digital electronics rather than the outdated analog functions of yesteryear.