To be able to walk and chew gum is an informal and often humorous way of saying one can perform two unrelated actions simultaneously. When it comes to playing the fiddle, this is easier said than done.
I can practice a basic tune with just my bow hand playing the strings, without fingering the notes with my left hand, and glide between strings, seldom hitting the wrong string or playing two at a time, keeping the bow nice and straight, and producing a rich tone. Likewise, I can put my bow down and finger the same tune with my left hand on the fingerboard, going through each note in order. Put the two together, and I have a problem walking and chewing gum!
As a beginner, it is difficult to coordinate bowing and fingering at the same time. With my right hand and arm…hold the bow properly, not too much or too little bow pressure, keep the bow parallel to the bridge, move fluidly from one string to another without hitting both, all while producing a good sound, not one like a screeching cat. With my left hand and arm…move the left hand up and down the fingerboard, finger the proper note, on the proper string, in the proper place, and at the proper time. Whew!
Remember as a kid trying to pat your head while rubbing your belly in a circular motion at the same time? How did that work out? I can do that now, but it took time and practice, and so it will with my fiddle.