In linguistics, borrowing is a term for various processes by which speakers of one language incorporate features from another language into their speech. It is most frequently used in referring to
Lexical borrowing
---the use of a lexical item (word or phrase) from another language without any phonetic indication of its foreignness. Sometimes speakers may attempt to conceal borrowing by modifying the foreign words or phrases in question to fit the phonotactic constraints of the language of discourse (this process is called nativization). In any case, the item's original semantic value (i.e. what it means in the language it's from) is preserved.
Bilinguals and people just learning a foreign language engage in lexical borrowing all the time, occasionally to hilarious effect. My advisor tells a story of one conversation she had with a friend and some elderly aunts in Spain. In the middle of extolling the virtues of Spanish bread, she couldn't remember or didn't know the word for preservative (whatever; the linguistics term for a word you don't know or can't remember is lexical gap) and took a guess: preservativo (apologies for my Spanish spelling or lack thereof). Later, after the aunts had left, her friend expressed surprise that my advisor could just casually talk to her aunts about preservativos. Turns out what had seemed like a safe guess was the Spanish word for condom. But I digress.
Lexical borrowing can be a source of new words in that a frequently-borrowed lexical item may be absorbed into a language as a loanword. It is the most often discussed form of borrowing because it is easily detected and its longterm effects easily traced.
Other types of linguistic borrowing include
Syntactic borrowing
---which to be perfectly honest I really don't understand, so it's hardlinked to encourage anybody who has a clue to add more information. What I know is that when two or more populations that speak different languages come into contact for social, political, economic, or other reasons, the languages involved tend to change more rapidly than languages in isolation. Under contact conditions, syntactic (i.e. grammar-related) changes occur, as does the formatin of loanwords and various phonetic effects, and the pidgin or even creole languages that sometimes arise from language contact tend to have simpler grammars than older, more isolated languages, which have generally evolved increasingly complex syntactic structures over time. | 
