Certain impersonal expressions as it is possible, it is impossible, it is surprising, it is urgent etc. require the subjuntivo.

Es posible que haya llamado, pero no estaba en casa.	Possible that he had called but I was not at home
Es imposible que no se haya dado cuenta de lo caro que es.	Impossible that he didn't notice how expensive it is.
Es muy raro que no me llame.	It is strange that he doesn't call me.
Es extraño que no me haya dicho nada.	It is strange that he didn't tell me about it.
Es necesario que cada uno haga lo que mejor pueda.	It is necessary that everyone do what he can do best.
Es preciso que venga mañana.	It is necessary that he come tomorrow.
Es maravilloso que esté recuperado ya por completo.	It is wonderful that he is already fully recovered.
Es probable que se quede sordo para el resto de su vida.	It is probable that he stays deaf the rest of his life.
Es mejor que te vayas ahora.	It is better you leave now. (You'd better leave now.)
Conviene que alquiles este piso, porque de momento no vas a encontrar otra cosa.	It is convenient that you rent this apartment now, because you won't anything else.
Es imprescindible que lo pages ahora mismo.	It is absolutely necessary that you pay right now.
Puede ser que me lo haya dicho, pero lo he olvidado.	He may have told me but I have forgotten about it.
Vale la pena que lo preguntes, a lo mejor lo sabe.	It may be worth asking him, maybe he knows.
Hace falta que le des el dinero, si no se va a morir de hambre.	You need to give him money, otherwise he'll starve (die of hunger)
Es peligroso que tengas tanta confianza en él, te digo que va a abusar de ella.	It is dangerous that you have so much trust in him, he will abuse it.
Es mejor que lo hagáis vosotros mismos, entonces vais a estar seguros que está bien hecho.	It is better you do it yourselves, this way you'll be sure that it is done well.
Es importante que lo veas, te juro que te va a impresionar.	It is important that you see it, I swear you'll be impressed.
Es importante que hagas lo que realmente te gusta.	It is important that you do what you really like.
Es poco probable que no se haya dado cuenta que su comportamiento era inaceptable.	It is unlikely that he noticed that his behaviour was unacceptable.
Es necesario que no hagas siempre lo que te dice, tú mismo tienes que saber lo que te conviene.	It is necessary that you not always do what he tells you to, you yourself must know what's convenient for you.

On the contrary the is not used when the impersonal phrase describes a fact or something that the speaker considers a fact.

Es seguro que no hay persona más testaruda en el mundo que él.	It is for sure that there is no person in this world more stubborn than he is.
Es verdad que ella es una hermosura.	It is true she is a beauty.
Es cierto que ha perdido su trabajo.	It is for sure that he lost his job.
Es evidente, que estos dos no se llevan bien.	It is obvious that the two of them do not get along.
Está claro que con lo que ganas, no puedes alquilar la casa.	It is clear that with the money you earn, you cannot rent this house.
Es indudable que él es una persona generosa y amable.	There is no doubt that he is a generous and loveable person.