at large

be at large:
If someone dangerous is at large, they are free what they shoud not be.

-from Cambridge Advanced Learner's Dictionary

Could you explain how this phrase came to have that definition logically?

I'll appreciate it!

Quick Google search turns up this (can't speak for its authenticity, but it sounds plausible enough):

"An obsolete meaning of "large" as a noun is "freedom, liberty," now surviving only in the phrase 'at large" (Webster's unabridged, 1934)."

That's from the Phrase Finder, which may be a good reference for you to save for other questions:

http://www.phrases.org.uk/bulletin_board/8/messages/536.html