The idea of Esperanto is: the foundation of a neutral language will help break down barriers between people and help everyone see each other as neighbors. [L.L. Zamenhof, 1912]
The basic idea of Esperanto is about tolerance and respect for people of diverse nations and cultures. Communication is indeed the essential part of understanding each other, and if that communication happens through a neutral language, that can help the feeling that we 'meet' on equal grounds and help create respect for one another.
As an ordinary speaker of Esperanto, you don't often think about the "foundation of a neutral language" and those kinds of fancy expressions. You just enjoy having the ability to express yourself freely in conversations with people from other countries and cultures.