Imagine you have a favorite toy that you always keep with you. This is your associated toy.
Similarly, when two countries decide to work together and share certain responsibilities such as defense or economic trade, they become an associated state. This means that they have agreed to cooperate and work together on some things, while still remaining separate countries with their own governments and laws.
Think of it like having a best friend. You both have your own families, houses, and teachers, but you still choose to do some things together like play at the park or share your lunch. Likewise, associated states work together on some things, but still have their own way of doing things in other areas.