To assist people is to help them out: to work with them, so that they can do something, or do something faster or more easily.
You can assist a person, or assist with some job or task. You could assist someone by bringing them what they need. If you help someone get their work done, you're an assistant--and you're giving assistance.
It looks like this rooster is assisting this dog! The dog wants to reach the food, and he can do it with the rooster's assistance.