check on (someone or something) means to look into their/it's condition.
"I'm going to check on things at the factory. I hope everyone is still working hard."
"I'm going to check on my sister and make sure she is doing her homework."
check out (someone or something) means to evaluate them/it.
"I'm going to check out the competition and see how we compare."
"Check out Maria's skirt! It's so cool."
"Check out" can also have other meanings, such as "to leave/depart" "I'm checkin' out, friends, see ya later." Or, to take something someone away: "May I check out this book?" (from the library) "I'm here to check my daughter out of school, she's feeling unwell."
For a more thorough answer "check out": http://idioms.thefreedictionary.com/check+out