As you play the game, people come in and make orders, each of which requires a certain number of icons to make (7 beef, 5 tomato and 6 lettuce, for example). Making matches on the grid removes the matched tiles from play (with cash bonuses for combos). Once enough of the icons have been matched to complete the burger, it becomes ready for you to click on - this gives it to the customer and produces the cash. Up to four orders are produced at once - when the first burger has enough beef (for example) any remaining matches go onto the second one. Customers are impatient - the value of an order drops as you take too long, and angry customers can leave without paying once their patience runs out.
What good would a burger joint be without chips or drinks? None, so they are implemented in Burger Rush, as bonus items. Matches made on the game board gradually fill the drinks and chip machines, and once ready those items can be added to an order, so as to produce bonus cash.
The game board also contains tokens, which you can collect and then spend in the shop after each level. New more-profitable recipes can be bought, as can upgrades to you drinks and chips machines (which allow these to be produced more quickly, and for more profit each time). You can also buy sweets, cookies and apple pie, which can be given to customers to restore their moods.