'Siddhi' means accomplishment or fulfillment 'marvellous skills or capability'-Sarvasiddhi pradaaya means 'To Him who grants all accomplishments and skills'. Through Baba's grace, the blind see, the mute talk, the lame walk, the bed ridden move about and the morons become intelligent. So, He is the energy behind all activity.
'Siddhi' also means specifically the super-human power, attainable through Raja Yoga as mentioned in Patanjali's Yoga Sutras. The Siddhis can also be attained, according to Patanjali, with birth or by drugs, Mantras, thapas and Samadhi. The siddhis which could be got by Thapas are those that are granted by Bhagwan Sathya Sai Baba.
He can confer them also by His own will and initiative, by sheer grace. Baba, of course, has all the Siddhis at His beck and call, because He is the source of all power, human and superhuman. So, when any one prides Himself as the master of any superhuman skill, he is only announcing that he has secured Baba's grace. Baba is the giver, though the recipient may not know or does not care to acknowledge it. His Anugraha (grace) can overcome the Navagraha (Nine planets) and transmute Manava (Man) into Madhava (God).