Nazir, Chapter 2, Mishnah 5. A person who completes his term of nezirus is obligated to bring three offerings:
A chatas (sin offering).
An olah (burnt offering).
A shelamim (peace offering).
A nazir becomes obligated in these offerings automatically upon completing his nezirus. However, a person may take upon himself to provide these offerings on behalf of someone else - on behalf of another nazir. That is the case our Mishnah discusses.
The words of the Mishnah and their explanation:
"Hareini nazir" - a person vows and accepts nezirus upon himself.
"V'alai l'galei'ach nazir" - and in addition, he accepts upon himself to provide for the shaving of a nazir.
As part of the process of bringing the offerings at the conclusion of nezirus, the nazir shaves his head, and because the bringing of the offerings is accompanied by the shaving of the head, the offerings of nezirus are referred to as "shaving." But the intention is to the offerings themselves, since the shaving involves no expense at all, whereas bringing the offerings costs money. So this person has accepted upon himself to provide the offerings of a nazir.
"V'shama chaveiro v'amar: Va'ani" - his friend hears his vows and says: I too accept this upon myself. The word "va'ani" refers to accepting the vow of nezirus.
"V'alai l'galei'ach nazir" - and I too accept upon myself to provide for the shaving of a nazir, meaning the offerings of a nazir who is completing his nezirus.
"Im hayu pik'chim":
"Im hayu pik'chim - m'galchim zeh es zeh": if these two men are clever, each one will provide his friend's offerings. In this way they will not end up obligated in more than what they originally accepted upon themselves - the nezirus alone, since the first provides the offerings for the second and the second for the first.
"V'im lav - m'galchim nezirim acheirim": and if for whatever reason they did not want to do this, or they did not think of it, they must provide the offerings of nezirus for other nezirim who need someone to provide their offerings for them.
In summary: in this Mishnah we learned about a person who vowed nezirus and also accepted upon himself to provide the offerings of another nazir, and his friend accepted both of these upon himself just as he did. If they are clever, they shave one another, and each one bears only the expenses of the nezirus that he accepted upon himself; and if not, they must provide the offerings for other nezirim.