The slot game payline is a line that runs from one side of the slot window to the other.  When the wheels stop spinning, the icons under the payline must match a specific pattern or combination of symbols in order for you to win.  Unlike the early of slot machines, modern slot games do not just have a single center payline that runs straight across the window.  The payline can have many different shapes, zigzagging across the screen through the all icons.  Betting on multiple paylines will greatly increase your chances of winning.
Gambling experts always recommend betting as much as you can as the higher payline combinations usually have slightly higher payouts than the lower numbers.  If you can’t afford to “bet max” on the machine you like then see if you can change the base wager amount.  Most modern slot games allow you to bet anywhere from a penny to several dollars per line.  Find a level you’re comfortable with and bet max, baby!