Goals are simply objectives that are displayed on the top ribbon of the Main Game screen. Each Goal provides you with a bar at the bottom of its button indicating your progress and in the bottom right is the type of Reward you will earn.
Remember different goals can provide different Rewards
Every chapter comprises a number of goals that you must achieve to move on to the next Chapter. When the required number of goals have been achieved, the Goals progress bar will be replaced with "Chapter # Completed" status and a "Next Chapter" button. You can tap on the "Next Chapter" button, play the Getaway mini-game, and start the next chapter; OR you can still continue playing and achieve more goals to get more rewards and increase the inventories, so don't miss those goals, especially the easy ones.