Contractions compress two written words into one, and the apostrophe marks exactly where letters dropped out, so a reader can rebuild the full phrase.
Take do not: join the words, drop the o, and the apostrophe sits in that gap, giving don't. The same move explains many everyday pairs: I am becomes I'm because you join the words and leave out the a, with the apostrophe marking that gap. As long as you can say which letters disappeared, you can build the contraction and read it back to the full phrase.
Some forms are irregular, like will not becoming won't, so the omission rule does not explain every contraction.
Try it yourself: read the phrase do not aloud, then say don't, and notice which sound disappears. If don't matched the full phrase, you have got the pairing; if something else came out, compare the two again and look for the missing o.
Watch the same words merge step by step. Start with do not, slide them together into donot, then delete the o between n and t. The apostrophe drops into that exact gap, so don't carries a visible record of the letter that vanished.
The apostrophe works like a bookmark in a folded page: it holds the place where letters were removed, so a reader can unfold the phrase back to do not. Because the mark sits where the omission happened, the shape of the contraction stays predictable.
The same case shows why this matters. Read I don't know and you can rebuild I do not know without guessing, because each apostrophe tells you precisely which letters were squeezed out during the merge.
This pairing by example extends across many everyday forms: I am becomes I'm, they are becomes they're, and you cannot becomes you can't, each time with the apostrophe marking the dropped letters.
One limit to keep in mind: not every contraction follows the omission rule cleanly. Will not becomes won't, where the vowels change rather than simply disappearing, so some forms must be learned as pairs rather than derived.
Will not becomes won't, and this one works differently. Because willnot would sound wrong with no vowel in the middle, the i changes to o instead of simply vanishing. The apostrophe still stands for the missing letters, but here it covers both a deletion and a vowel change, which is why won't does not match the neat letter-for-letter pattern of don't or I'm.