It's very closely related to the development of the QWERTY layout we see on most keyboards, which began with typewriters in the late 1800s.
Early QWERTY typewriters omitted the digits 1 and 0 because letters l (lowercase L) and O (uppercase o) looked close enough/identical in their font. Basically, you could just type a letter l or O and it would look close enough.
Fewer keys on the keyboard would have been easier and cheaper to manufacture - the mechanical linkages were rather complex, and as you add more keys, you run into issues with lack of space and clashing keys.



0 was added in a revision before they bothered adding 1, and 023... would have looked odd, so it was added to the end of the number row, after the 9.
A potential reason for adding a 0 but no 1 is because an uppercase letter O for the digit 0 requires the use of the shift key, which is less convenient than the lowercase letter l for the digit 1. Again, they tried to minimize the number of keys.
Then a 1 was added to the beginning of the number row.
https://ux.stackexchange.com/questions/76446/why-is-the-0-next-to-9-not-next-to-1
https://www.reddit.com/r/explainlikeimfive/comments/35kfo0/eli5_why_does_0_come_after_9_on_the_keyboard_and/