Common stock is what you buy when you buy a ticker. It gives you a proportional claim on whatever is left after debt holders and preferred-stock holders are paid, plus a vote at the annual-meeting on directors and major proposals. There is no promised payment: a dividend is declared at the board's discretion and can be cut.
For a trader the practical points are that common stock is the most liquid layer of the capital structure, it is the layer options are written on, and it is the layer that gets wiped out first in chapter-11.
Example: a company has assets worth $500M and debt of $450M. Common holders have a residual claim on $50M. If asset values fall 12% to $440M, the debt is not fully covered and the common is worth nothing in a liquidation, even though the business only shrank by an eighth.
Related: preferred-stock, voting-rights, outstanding-shares