The most prominent characteristics of common stock are that they entitle the shareholder to vote on corporate matters (typically, the shareholder gets one vote for every share he or she owns, though that is not always the case) such as whether the company should acquire another company, who the board members should be and other big decisions. Common stock also often comes with preemptive rights, which means the shareholder has a "right of first refusal," or first dibs on buying any new stock the company tries to issue.
Perhaps the most important attribute of common stock is that their holders are the last in line when it comes to getting their money back. If the company goes bankrupt and has to sell off its assets, the cash from the asset sale first goes to lenders, employees and lawyers. The shareholders get whatever is left (which is usually nothing, or just a few pennies for every dollar they originally invested).