'Garbha' means womb, 'Sanskaar' means Value education. 'Garbha Sanskaar' thus implies education inside the womb.
Facts behind it:
Our Ayurvedas, call it 'supraja janan', in which the couple can plan well in advance the, education they would like to impart to their child (Precisely three months in advance). 'Garbhasanskaar' is all about being in a good state of mind - emotionally, spiritually and being physically fit. It is ritually followed by the Indian families since ages, but now it is also being adopted by the west in a big way.
60% of the brain of the child is developed, while he/she is in the womb of the mother. Scientists say, a child's mind is developed based on the mother's mental state. If a mother is happy and does things that enriches her mind, like reading, the unborn child is being passed wisdom already.
We have a lot of Indian mythology related to 'Garbha Sanskar'. A famous one is of prince Abhimanyu in the epic Mahabharata. Arjuna's wife was pregnant with their son Abhimanyu. Once Arjuna was telling her the strategy to penetrate the 'chakravyuh' (a type of arrangement of soldiers by the opponents during war). It is said that she dosed off when he was narrating the exit process. Abhimanyu, ironically, was in a war situation wherein he was faced with a 'Chakravyuh'. Even without formal training about this technique, he could broach it but didn't know how to exit and thus got entrapped (as he had heard only half the story even inside his mother's womb).
How does it work?
Umbilical cord is the direct connection between the mother and the child. Communication to the mother is the communication to the child as well. Those extra nine months are invaluable even from a mental development point of view. Feelings, hunger, emotions, stress et al that the mother goes through, the baby in the womb also feels a part of it. A mother can communicate to the baby just by caressing her hand on her belly and talking to him/her. Believe me, this works wonders. I also call it the unique 'Mumma-Baby' bond.
A mother can impart good qualities ('Sattva Guna') in the baby right after conception. Talking to the unborn child every day, asking him/her to be kind, noble, polite, loving, caring, sharing etc will definitely make the baby what you wish it to be.
Music, Mantras and Meditation. Listening to soothing music can make the baby calm and settled in nature. It lends a lot of peace to the mother and the unborn child. Chanting your devotional mantras and prayers will subtly help impart 'sattva guna' automatically. It also helps drive away negative thoughts from the mother's mind. Negative thoughts are not good for the baby inside the womb - it gives them a feeling of fear and anxiety, which they will carry with them throughout, even once they are out in this world. Meditation helps keep the mind and body relaxed, enables mother and baby to be focused and also prepares the mother to be strong mentally for the delivery.