To give courage to; to inspire with courage, spirit, or hope; to raise, or to increase, the confidence of; to animate; enhearten; to incite; to help forward; -- the opposite of discourage.

inspire with confidence; give hope or courage to

To give reassurance, stimulation, support, inspiration etc to someone either during or at the completion of a task.

spur on; "His financial success encouraged him to look for a wife"

Stimulate; give help to; foster.

contribute to the progress or growth of; "I am promoting the use of computers in the classroom"