Imagine 1 ping pong ball in your cupped hands. Now toss it up real high and let it land. It'll fly up, separate, come down, and scatter. Now, how many ways can you imagine it going? Pretty easy, because if you tossed it up, it'll come back down and you can track it pretty easily.
Now repeat that thought experiment with 10 ping pong balls. How many ways can you imagine those 10 ping pong balls going? Almost impossible right?
Entropy is a measure of the randomness/disorder represented by the 10 ping pong balls. The number of ways the ping pong balls can be arranged is how we measure the randomness of a system.
Now consider two atoms bonded. Say, two Hydrogen atoms (H-H). These two hydrogen atoms are bonded, and as a result we can somewhat predict the position of the atoms right? If we know where one is, we can be sure the other one will be right next to it because they are connected.
Now let's break that bond. The two hydrogen atoms are now free floating in space, and we can't as easily predict the position of the atoms anymore. If we know where one is, all we can be sure is that the other atom does not somehow occupy the exact same position in three dimensional space. In that sense, we have increased the randomness/disorder of the system, aka entropy, by breaking that bond.
Now let's try to create that bond again. We have to add some energy to create that bond though. But once we add the energy to the system and create that bond, we now have decreased the randomness/entropy because now we can predict where one hydrogen is based on knowing where the other one exists.
Hopefully that helps you better understand both entropy and the Gibbs free energy equation (deltaG = deltaH - Temp*deltaS). By increasing energy, G, by creating a bond, we can force a decrease in S, entropy. By lowering the energy, G, by removing bonds, we then cause an increase in S, entropy.