Basically, brahmacarya means celibacy.

karmana manasa vaca
sarvavasthasu sarvada
sarvatra maithuna-tyago
brahmacaryam pracakshate

“The vow of brahmacarya is meant to help one completely abstain from sex indulgence in work, words, and mind—at all times, under all circumstances and in all places.” (-Yajnavalkya-smriti, as quoted in Bg. 6.13-14)

There are eight aspects of brahmacarya, as described in Shridhara Swami’s commentary on Shrimad-Bhagavatam 6.1.12:

smaranam kirtanam kelih
prekshanam guhyabhashanam
sankalpo ‘dhyavasayash ca
kriya-nirvrittir eva ca

One should not:

1. Think about women.

2. Speak about sex life.

3. Dally with women.

4. Look lustfully at women.

5. Talk intimately with women.

6. Decide to engage in sexual intercourse.

7. Endeavor for sex life.

8. Engage in sex life. (SB 6.1.13 Purport)

One who practices brahmacarya is called a brahmacari. In the varnashrama system, the brahmacari-ashrama is the first of four, namely, brahmacari, grihastha, vanaprastha, and sannyasa.

“According to Vedic principles, the first part of life should be utilized in brahmacarya for the development of character and spiritual qualities.” (SB 3.22.19)

Brahmacarya is thus student life. It was traditionally rigorous, disciplined, and austere. It is a life of cultivation, of preparing for the future. In all ashramas devotees are cultivating Krishna consciousness, preparing for the examination of death. But the brahmacari period is specifically meant for training: training in how to control the senses and subdue the mind; training to be a grihastha, vanaprastha, and sannyasi. This training is by submission to, service to, and friendship to the guru. (SB 7.12.1)

In terms of varnashrama principles, the highest standard of brahmacarya means the vow not to marry but to observe strict celibacy throughout life. (SB 7.12.7) This is called the brihad-vrata (“great vow”), or naishthika-brahmacarya. “Naishthika-brahmacari refers to one who never wastes his semen at any time.” (SB 3.24.20) “The word maha-vrata-dharah indicates a brahmacari who has never fallen down.” (SB 6.17.8)

In Indian society, brahmacarya has often been considered as a set of restrictions aimed at upholding good health and moral principles, with the ultimate purpose of enjoying civilized sense gratification. Brahmacarya in Krishna consciousness, however, operates on the dynamic principle of knowledge and renunciation fully engaged in the service of God. Shrila Prabhupada: “One practicing brahmacarya should be completely engaged in the service of the Lord and should not in any way associate with women.” (SB 4.28.3) According to the definition of brahmacarya given in Shrimad-Bhagavatam (7.12.1), an unmarried person who does not live in the guru’s ashrama, who has not submitted himself to the rigid life of surrender, and is not directly and exclusively engaged in the service of his guru, cannot properly claim to be a brahmacari.

The broader meaning of brahmacarya is brahme carati iti brahmacarya: “To act on the spiritual platform.”