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Having suitable skill in multiple things, but not being an expert in any of them.
The word 'jack' can refer to the common man. Thus, a 'jack of all trades' meant a man who is competant at many different skills. The first half of the phrase was being used in the 1600s, and was apparently spoken in a complimentary fashion when describing people.

An early example comes from a book published in 1612, titled Essayes and characters of a Prison and Prisoners. The book was written by Geffray Minshull and reads:

"Some broken Cittizen, who hath plaid Jack-of-all-trades."

From what I could find, it looks like it was somewhere around the 1800s when the expression developed a less praiseful meaning, as that was when the 'master of none' part was attached to it. This can be seen in in The Atlas newspaper from 1828, where it reads:

"You rarely meet in England a man who is Jack of all trades and master of none."

Both forms of this saying are still heard today.
Note: The origins for most idioms and common phrases cannot be said with a certainty. What's provided are theories that may be plausible to how a phrase originated, but not necessarily so.

In addition, quotes that contain a particular phrase may be taken from old newspapers, poems, or books that were written centuries ago, but this by no means confirms that the phrase originates from said newspapers, poems, or books. In all likelihood, if an expression is being used in a newspaper, it's probably already a well known saying and is from an older time.
* I was planning on earning an associate's degree in numerous subjects, but my family suggested to not be jack of all trades and master of none, so I had to rethink my future plans with college.
The meaning of this phrase.
The origins of this idiom.
Know Your Phrase - The Meaning And Origins For Phrases and Idioms > J-Letter Sayings