Mula Bandha or Moola Bandha is perineal lock or seal at the base of the pelvis and when engaged it enlivens muladhara chakra. In addition, it helps in maintaining and direct upwardly the pranic or life energy flow within the body.
In the process of learning mula bandha, one will encounter and engage vajroli/sahajoli mudra and ashwini mudra. Vajroli is related to men, Sahajoli is related to women, and Ashwini is engagement of the rectal sphincter muscles.
Often there is confusion between these three practices. Basically, mula bandha is engaged to awaken muladhara chakra. Mula means "root" or "foundation" and is the base from which we grow and evolve as human beings. It is the seat of our security, as well as, excretory, urinary, sexual and reproductive organs.
Vajroli/Sahajoli and Ashwini mudras awaken swadhisthana chakra. Swa means "one's own" and adhistana means "dwelling place". Swadhisthana is related to the procreative processes and the urinary system. In addition, it is said this chakra is the seat of the unconscious mind, which is the storehouse of our mental impressions and previous experiences (be those in this lifetime or potentially previous ones).
To better understand these three elements in the body, here is a diagram from the Bihar School of Yoga illustrating the position of Mula Bandha, Vajroli/Sahajoli and Ashwini Mudras.