Rebracketing is a phenomenon in languages where the boundaries between two words can become lost, and then reappear in a new place.
A major source of this in English is the mutability of our indefinite article, which may be 'a' or 'an', depending on whether the noun to follow begins with a vowel.
So a simple example of this would be the word orange. This is a very old word which came to us during the Renaissance from an Indian language - possibly Tamil or Malayalam. Back then, it was more like 'norange' but of course it lost the 'n'. Or rather, the 'n' moved:
A norange -> An orange -> Orange
This applies to many words, including ones like apron (napron). It can even go in reverse:
An ewt -> A newt -> Newt
We do it with nicknames, too:
Eleanor -> Elle -> Mine Elle -> My Nell -> Nell
Nell isn't a very common nickname now, but it used to be popular for Eleanors! (Consider bringing this back if you are an Eleanor).
Other examples stem from the mild confusion which results from bringing a portmanteau from one language into English. Here are some examples of that:
Hamburg + -er -> Hamburger (denoting someone from Hamburg, but also a food)
Hamburger -> Ham + Burger
Cheese + Burger -> Cheeseburger
Here, we have broken the word up where there is a gap between syllables. It makes sense to us, but it is etymologically silly!
Other examples of this include:
Cybern + etics -> Cybernetics Cybernetics -> Cyber + netics Cyber + space -> Cyberspace
Once again, it's an 'n' which is moving, but this time it's unrelated to the article.
Another related phenomenon is called 'juncture loss'. This often concerns articles again, but in other languages.
For example, the Greek expression 'hoi polloi' which literally means 'the many' (compare 'polloi' with the prefix 'poly-' as in 'polyamory', 'polysaccharide', etc.).
Posh English people (for whom education in Greek was a class marker) borrowed this expression to refer to the working class, with derision.
However, they brought the article ('hoi') with the noun, resulting in the lignuistically redundant phrase, 'the hoi polloi' (literally, 'the the many').
Another example is the Arabic phrase 'al kuhl', which came to refer to various distillates.
I think a reasonable translation is 'the powder'.
It passed through French and is preserved in the modern English word 'alcohol' ('the the powder').
Notice that the Arabic article, 'al', has come with it.
There are many more examples of this phenomenon, but I think this covers the subject well enough for the moment!