STEEM Power (SP) is STEEM (cryptocurrency) that has been locked in, vested, meaning it can't be immediately withdrawn to spend.
STEEM Power is what gives an account influence on Steemit.  The more SP an account have, the more money can an account give to authors with an upvote. The curation rewards also increases for the voter. There is a very small 'interest' rate earned by holding STEEM Power.
Converting STEEM to SP is called powering up. This can be done in a steem wallet by using an active key. STEEM Power gives an account Resource Credits (RC) which are needed for broadcasting all kind of operations. 4 SP is for example needed to write one small comment a day. If an account has more SP, it can broadcast more operation per day.
Converting locked STEEM Power back to liquid STEEM is called "Powering Down". A process which moves 1/13th of the STEEM Power every week back into STEEM. The Powering Down process is completed after 13 weeks and can be stopped any time.
So for example, if an account has 1300 STEEM Power. Powering down will release 100 STEEM after a week.
STEEM Power can also be delegated to other users. Delegated SP increases the influence of the receiving user to the same level as if he owned the STEEM Power himself. However, the delegator remains in full control of the delegated SP and can take back a delegation at any time. Delegated SP cannot be powered down, neither by the delegator nor by the receiver. When SP is undelegated, it immediately reduces the influence of the former receiving user, but takes 5 days until the SP is available again to the delegator.
STEEM Power is internally called VEST. The amount of VESTS an account holds is fixed. The inflation is implemented as a conversion rate which decreases over time. Thus, more STEEM can be returned when it was converted to STEEM Power a while ago.