An American Idiom
essentially meaning that one is incapable of or klutzy when performing a certain task by hand. Generally, though, it's used to refer to a clumsy
person, or someone with no dexterity.
The best example to illustrate this is one's experience with learning to tie a shoelace. Your fingers trip horribly all over one another initially and you feel like an incompetent clod for most of the time learning.
Now here's a fun visualization to really drive the point home. Look at your fingers. Notice the extra joint on all fingers except for your thumb. Now, visualize ALL of your fingers having the same joint structure. With that in mind, *now* try and tie your shoelace. *snicker*
All thumbs? Unfortunately, Some people feel like that *all* the time, with everything they do.
Useful point of interest: this phrase with old English roots was first recorded in John Heywood's Proverbs: "Whan he should get ought, eche fynger a thumbe."
Props to the QPB Encyclopedia of Word and Phrase Origins