A siddha in Sanskrit means "one who is accomplished" and refers to perfected masters who according to Hindu belief have transcended the ahamkara (ego or I-maker), have subdued their minds to be subservient to their Awareness, and have transformed their bodies composed mainly of dense Rajo-tama gunas into a different kind of bodies dominated by sattva. This is usually accomplished only by persistent meditation over many lifetimes.
A siddha has also been defined to refer to one who has attained a siddhi. The siddhis as paranormal abilities are considered emergent abilities of an individual that is on the path to siddhahood, and do not define a siddha, who is established in the Pranav - the Aum, which is the spiritual substrate of creation. The siddhi in its pure form means "the attainment of flawless identity with Reality (Brahman); perfection of Spirit."
The concept of siddhas is a prime notion in Jainism.

Tamil Nadu tradition of Siddhahood

Agastyar
Tirumular
Siddha Sampradaya
Siddha Yoga
Siddhi
Mahasiddha