Your carry on bag is the one that you are going to take with you through the security checkpoint and onto the airplane. All airlines limit you to 2 carry on items, 1 bag plus 1 personal item. Your personal item would be a backpack, briefcase, laptop bag, purse, or camera bag for example. These items usually have to fit under the seat in front of you (an area that can be as small as a shoe box).
Your other carry on bag can go into the overhead bin. Roller board suitcases are the most common bag but some people choose duffel bags, trolley bags, or even large travel backpacks. The size of your bag is limited by the size of the overhead compartments. The standard size seems to be 22 inches (the height of the bag) so that it can fit inside the bin with either the wheels or the top handle facing the aisle of the aircraft. If your bag does not fit in the overhead bin it will have to be checked and you will have to pay the appropriate fees.
One thing to be aware of is how much your bag weighs. Make sure it is light enough that you can lift it above your head. By law flight attendants are only required to help lift bags of passengers with disabilities. Due to the potential for on the job injuries most airlines either forbid or discourage employees from helping passengers lift bags.