If anyone has in his possession a sacrificial animal to offer as a sacrifice (on 'Id al-Adha), he should not get his hair cut and nails trimmed after he has entered the first days of Dhu'l Hijja
The Book of Sacrifices - Sahih Muslim 1977e
This prohibition applies from the beginning of Dhul-Hijjah until after the sacrifice has been offered. The wisdom behind this ruling is to maintain the completeness of one's body during the sacred period, as the sacrificial animal represents the person offering it.
Scholarly Commentary
The prohibition includes hair from all parts of the body and trimming of nails. This ruling applies specifically to the one who intends to offer the sacrifice, not to other family members unless they have their own designated animal.
If someone forgetfully trims hair or nails during this period, they should seek Allah's forgiveness but their sacrifice remains valid. The prohibition ceases once the sacrifice has been properly offered.
Juridical Rulings
The majority of scholars consider this prohibition to be strongly recommended (mustahabb) rather than obligatory. However, it is best to adhere to it out of precaution and following the Sunnah.
Shaving due to necessity (such as medical treatment) is exempted from this prohibition. The essential act of sacrifice remains valid regardless of this matter.