Prices and wages are "sticky" if they do not immediately rise or fall to reflect changes in demand and supply. For example, suppose the price of tomatoes increases, raising costs for the owner of an Italian restaurant. The owner would like to charge more for the meals that he serves, but doing so requires him to print a new set of menus. The owner may decide that the cost and hassle of redoing the menus is not worth it, and keep prices unchanged. In this case, the price of an Italian restaurant meal is sticky.
Similarly, suppose a worker as a 3 year wage contract with her employer. Even if many other workers become unemployed and the employer finds that he could now hire workers for less pay, the employee is guaranteed a fixed wage in her contract. This is a sticky wage.