Simply put, your mission is to be absolutely happy, happiness that does not depend on circumstances but comes forth through your own Buddha nature manifesting. At the same time, enabling others to do the same. In this Saha world which is full of suffering and negativity, in order to do that one needs to "demonstrate" to others how.
This is where our desires and social roles come into play. To create value as a family member, doctor, teacher (pick your profession), to be able to create value in other ways in society centered on Buddhist practice, etc is the "role" one plays to display the immense power of Buddhism and lead others to absolute happiness. Buddhism and daily life are one and the same.
To say that our mission as Buddhists is to escape Samsara (this world) or in other words to escape from the cycle of birth and death (wrongly interpreted as nirvana) is to be selfish. That is not the way a Buddha or a Bodhisattva thinks.
Shakyamuni Buddha says in the Expedient Means chapter of the Lotus Sutra -
"At all times, I think to myself: how can I cause living beings to gain entry into the unsurpassed way and quickly acquire the body of a Buddha?"
Note that Lord Buddha says that everyone can become a Buddha, and he says that at all times he exerts himself to enable others to become like him.
In short, to enable ourselves to reveal our Buddha nature and helping others do the same is our true mission as Buddhists.