Steem power and influence are the same thing here. You can 'power up' your steem directly into steem power (which is instant), and convert your steem dollars into steem to use for powering up (once you click 'convert', it takes a week before the conversion is complete). Note that this will make these (re-invested) funds unavailable for withdraw.
RE: Could someone explain Steem to me like I am a three year old?