Lexicalization is the process of raising something to the status of a
word. It means something that wasn't a word before, or wasn't expressed as a word, now is. It does
not normally refer to the
borrowing of an existing word from another language.
One way is when an acronym is treated as a word: SCUBA becomes scuba, RADAR becomes radar. Another is when a part of a word is elevated to independent status as a word. Usually the part is an existing prefix or suffix, such as photo, dynamo, retro, ism, or ology. But sometimes the new word was not originally a separable part of the word, such as pram from perambulator, or burger.
Hamburger was originally Hamburg + er. It was reanalysed as Ham + burger and the element burger was treated as a distinct morpheme, or meaningful component. I don't know which order this happened in. Possibly it was first abbreviated to 'burger and then new words were coined such as cheeseburger; or possibly the creation of words like cheeseburger gave the bound morpheme -burger, which only later began to be used as an independent word. So either the abbreviation or the bound morpheme was lexicalized. The word marathon illustrates the latter possibility: it has been re-segmented as if it contained a meaningful element -thon, which has then been used in telethon and nonce-formations like dance-a-thon; but so far the morpheme -thon has not been lexicalized. We don't talk about a thon, meaning a marathon event of some kind.
Noises can be lexicalized: miaow and tisk are spoken as normal words, not onomatopoeia, and have grammatical form: Tibbles miaowed. Basil tisked.
Phrases can be lexicalized: a bread-and-butter letter; a hit-and-run driver; an oh-so-cool attitude; a wannabe supermodel; the program contains several gotchas.
Differences can be lexicalized. In Anglo-Saxon times we both farmed and ate sheep, calves, and oxen. Then the Normans came and brought their French words mutton, veal, and beef for the meat they got on their tables. The difference between the animal and its flesh became lexical.
Grammatical functions can be lexicalized. I can't think of a good example in English for the moment, but let's say the use of shall and will for the future tense, which happened some time back in Proto-Germanic. Formerly the present tense would have been used for the future. The opposite process, grammaticalization, is probably a lot more common: such as the normal verb go coming to represent a future tense in the form going to.