won't /wəʊnt/ (BrE), /woʊnt/ (NAmE) is the contraction of will not.
She won't be late. Notice the spelling: won't, not willn't.
I won't forget your birthday. In speech, the vowel here is /ə/ in British English and /oʊ/ in North American English, so the whole word stays one smooth syllable.
Won't you come in? The /t/ at the end links neatly into you when you say it: /wəʊnt juː/.
The sounds /w/ and /əʊ/ point clearly to will, yet the standard spelling takes an o, so won't is the only standard form and willn't never became a word. The o is simply part of the historical contraction. Write the o even though the sounds do not demand it.
Won't belongs only to the verb will and expresses refusal or a negative future, as in The door won't open. Negatives of other verbs, such as shall not or don't, have their own forms and pronunciations.