"Jack" appears in literally dozens of phrases in the English language and has all manner of uses. Let me give a few examples: "Every man Jack of them" (= everyone of them); "Jack-in-the-box" (a toy in which a small male figure, on a spring, pops out of the box when the lid is opened); a "Jack" in card games (the servant of the King and Queen); Jack the Ripper (the name attributed to the unknown perpetrator of the Whitechapel murders of 1888); and a jack is a type of flag (smaller than an ensign and one flown from the jackstaff). There are many more..
Jack, as most of you will know, is regarded as the dimunitive of "John" and perhaps derived from the French "Jacques", given that the Normans came to Britain in 1066 and Norman French was the language used by the upper classes in Britain for several centuries. "Jacques", in the past, was apparently used to refer in general to a French peasant.
Jack is used as a generic name for any man and, for a long time, was a familiar term of address between workmen, sailors and the like. So, for example, "Jack Tar" is another word for a sailor (an ordinary seaman who, in the days of sail, got his hands blackened by the tar on the ropes). There was a nautical phrase, "Pull up the ladder, Jack, I'm aboard", which is clearly related to "I'm alright Jack". In both cases, it refers to being concerned with one's own self-interest without regard for the interests of others. Indeed, there is an Australian phrase, the Jack system, that means exactly that - pursuing one's own interests and welfare at the expense of others - and a master of the Jack system was sometimes called the President of the Jack Club.
"Jack of all trades" is interesting in that it can be used in praise of someone who can turn his hand to anything and everything (that is, someone who is versatile and willing to have a go at anything) but is often used disparagingly (someone who can never quite master any one thing).
Jack can also denote someone who is young or small (in the latter case, either actually small or small relative to something or soemone else). In the nursey rhyme "Jack and Jill", Jack is a young lad and, in "Jack and the Beanstalk" and "Jack the Giant Killer", Jack faces a giant. A "Jack the Lad" is a young man who is cocksure and a probably a bit flash. "Jack Sprat" is generally someone who is quite short, though a sprat is also something small, in this case a herring-like fish, so you get the double effect. In a similar usage, it can refer to someone who is inexperienced. The apprentice sheep farmer in Australia, for example, usually a young man but I think it can be anybody learning that trade, is called a jackaroo
As indicated above, a jack can also be a servant, so a boot-jack is a device for removing one's own boots, a task that, for rich people, would have been done by a servant in the past. As well as someone inferior, jack can refer to some thing that is small. Thus, the small target ball used in bowls, the small white ball to which you try to get closest, is called the jack. I don't know if there is an equivalent word in boules, bocce or petanque.
