Mudra is a sanskrit word meaning 'gesture'. They can be thought of as a seal for energy flow.
Some mudras are as complicated as involving the whole body through asana (posture), pranayama (breath), bandahs (energy lock) as well as visualisation. However the most common mudras are a simple hand position.
The text Asana Pranayama Mudra Banda says that mudras should be introduced later in practice, once proficient in asana, pranayama and bandha - as these practices help clear gross blockages.
Through practicing mudra, yogis develop awareness of energy flow through the body. It is said that mudras help to manipulate prana by diverting it to the upper chakras, as opposed to it leaving the body and dissipating.
In this same text there is a section on a scientific view point of mudras. It is explained that mudras act as a subtle, non-intellectual connection between the position of the hand and the mind. Different mudras set up different links and which effects the body differently. Over time repetition of the gesture can immediately bring the practitioner to a more refined state of consciousness.
One way to think of it is if you were to meditate over and over again with your hands in a certain position, your body learns than when you place your hand in this way, you will be meditating.
Eventually, whenever you take this hand gesture, your mind begins to go into meditation mode.
