Concessive conjunctions belong to the subordinate conjunctions. They express, in the subordinate sentence, an objection or difficulty for the accomplishment of what is stated in the main sentence. A few examples are: aunque, aun cuando, a menos que, siquiera, etc.

Let's look at some example sentences.

Aun cuando no esté de acuerdo, lo hace.
He does it, even if he doesn't agree.

Yo habría podido ver la película si hubiera hecho mis tareas esta tarde.
I could have seen the movie if I would have done my homework this afternoon.

Nosotros habríamos ido al parque si hubiera hecho sol.
We would have gone to the park, if it would've been sunny.

Salió de la casa no obstante su enfermedad.
He left the house in spite of his illness.

A pesar del frío, mañana iremos a la playa.
In spite of the rain, we will go to the beach tomorrow.