SpongeBob notices that he is very weak compared to Sandy and she offers to give him exercise training. After failing at it, SpongeBob goes home with painful arms. He lies in his arm, when a commercial on TV starts. Donald the Shark tells the audience why to buy the product. SpongeBob is then convinced and buys some. He goes to Goo Lagoon to show off his fake muscles. He convinces everyone, including Sandy. Thinking that he is really strong, she signs them up for an Anchor Toss competition. When it is SpongeBob's turn to go, the Anchor Arms started to break down due to SpongeBob overinflated them into the Jerk size while struggling to lift the anchor (even the Arms can be seen over-stretching with its "veins" bulging out and causes the air to blow up SpongeBob's body). Eventually, they burst and deflate, revealing that the muscles are just fake.
A variant of the anchor arms is used to repair SpongeBot SteelPants, after the real SpongeBob temporarily destroys him. The difference that this particular Anchor Arms appear to be made of plastic, instead of rubber balloon as in the original.
It is a reference to part of an anchor called the "arm," which is the part that curves out from the bottom end of the main part and ends in the pointed part.
In the scene where the Anchor Arms blow up, it is then deflating in a similar manner as a rubber balloon — floating randomly as it loses air and making a characteristic noise.
This is probably an oversight (or possibly for comical effect) since the Arms actually exploded, thus it would be completely blown up instead of deflating.
It is shown that SpongeBob appears to hide his real arms inside his body while using the Anchor Arms, as seen after the Arms get destroyed, he pops his arms out as Sandy looks at him.