Love helps you complete stages! See the bar at the top of the screen? The more you Love your pet, the faster it fills!
Petting your dog by tapping on the screen gives your dog love!
Upgrade Petting to increase the Love per Tap.
Buy assets like Food and Toys to give Love per Second.
Use the Ad Stage Speed Boost in the dark blue skills tab (with the timer on it) to x2 the speed that the stage bar fills.