Contractions - the act of replacing letters in words with an apostrophe - are often used in spoken English. It's easy to see where contractions such as "shouldn't" and "didn't" are short for, but a word like "won't" has rather less obvious origins.
The origins of the word "won't" are, in fact, pretty indicative of the long history of the English language. It's an evolved short version of "will not", originating back in the 15th century, when it was spelled and pronounced as "wynnot". As English continued to change over the years, it became "wonnot", and eventually was shortened to "won't". Strangely enough, "won't" never changed any further after that, even though for hundreds of years other English words and phrases have continued to evolve.
Contractions can be interesting in informal speech for the way they can stack - for example, "should not have" can be rendered "shouldn't've".
Native English speakers use contractions without even thinking, but rarely have the reason to question why they're so deeply ingrained in speech.