A purpose is somebody's goal or reason for doing something. In other words, a purpose is what a thing does, or why a person does what they do.
We could ask, what's the purpose of eyelashes? What do eyelashes do? Well, the purpose of eyelashes is to stop dust and other junk from getting into our eyes. That's their purpose: the reason we have them, the thing they do for us.
We could ask, why do ants always carry little things from place to place? What's their purpose for moving things around? What are they trying to do? Well, their purpose is probably to bring food home to their nest, or to move their stuff to a new nest.
In our kitchen, we keep the spices arranged in ABC order. Why? What's the purpose? Our purpose is to make it easy to find the spices we want.
(Source: original photo)
If you look inside the word "purpose," you can see how it has Latin bits that mean "(something) put or placed forward." The "pur-" bit means "forward," and the "pose" bit means "put or placed." Imagine that what you want is placed right in front of you, so you know what you're reaching for. You've got a purpose.
Something purposeful, or something done on purpose, is done for a reason. It's not done by accident or by mistake. When you do something on purpose, or when you do something purposefully, you knew what you were doing, and you meant to do it! There was no "oops" about it!
Someone threw a drink at this guy's face on purpose. They did it purposefully! (You can also say they did it "purposely," but that word is a little informal: it's fine to use it with your friends.)
Check out this guy's purposeful walk! When you know where you're going, you know what you're doing, you're standing straight and tall, and you're taking big, confident steps, then you have a purposeful walk. Your stride is purposeful. You might walk purposefully onto the soccer field, ready to play, or stride purposefully up the whiteboard, ready to solve a math problem.
If you have a purpose in life, or if you have a strong sense of purpose, that's wonderful. It means you know why you're alive! You know what you're doing with your life! You know what you want to accomplish in your life. You have purpose. And your life is purposeful.
The opposite of "purposeful" is "purposeless." Something purposeless is pointless: there's no reason for it. It's a waste of time! To me, it seems purposeless when a dog chases its tail. But what do I know? The dog must have its own purposes for doing it! And he probably thinks my spice drawer is purposeless!