Nazir, Chapter 3, Mishnah 1. The Mishnah deals with the question of when nezirus comes to an end: someone accepted nezirus upon himself, and we know that an unspecified nezirus lasts thirty days. On which day must he complete his nezirus - shave his head and bring his offerings?
"Mi she'amar hareini nazir" - an unspecified nezirus:
The Mishnah rules: "Megale'ach yom sheloshim ve'echad" - ideally he should shave his head and bring his offerings on the thirty first day, for only then does he hold thirty complete days of nezirus.
But the Mishnah continues: "Ve'im gileiach l'yom sheloshim - yatza" - after the fact, if he shaved his head and brought his offerings already on the thirtieth day itself, he has fulfilled his obligation. The reason is the principle of 'miktzas hayom k'kulo' - part of a day counts as a full day. Since he was a nazir for part of the thirtieth day, that is enough, for he accepted upon himself an unspecified nezirus.
"Hareini nazir sheloshim yom":
However, one who explicitly said that he is becoming a nazir for thirty days is not relying on the law of an unspecified nezirus; rather, he spelled out a number of days. The very fact that he specified teaches that he does not want a plain nezirus, but thirty complete days.
Therefore the Mishnah rules: "Im gileiach l'yom sheloshim - lo yatza" - even if he shaved after almost the entire day had passed, since a full day had not passed, he has not fulfilled his obligation of nezirus. This is because saying "thirty days" means thirty complete days, and in such a case we do not apply 'miktzas hayom k'kulo'.
In summary: In this Mishnah we learned the distinction between two formulations of accepting nezirus:
"Hareini nazir": Ideally he shaves on the thirty first day, and if he shaved on the thirtieth day, he has fulfilled his obligation, based on the principle of 'miktzas hayom k'kulo'.
"Hareini nazir sheloshim yom": Since he specified thirty complete days, if he shaved on the thirtieth day, he has not fulfilled his obligation, and we do not apply 'miktzas hayom k'kulo' in his case.