There is, there are

Hay is a very common Spanish expression. It is equivalent to the English expression "there is" or "there are:"

Hay un libro en la mesa.   There’s a book on the table.
Hay tres hombres en la clase.   There are three men in the class.
Hay muchas cosas a hacer.   There’s a lot to do (There are lots of things to do).

Hay is the present tense impersonal form of the verb haber, and can be followed by a singular or plural noun.

In other tenses and moods, the impersonal verb haber has both singular and plural impersonal conjugations, but most Spanish speakers consider use of the plurals as incorrect. I’ve provided both forms here for reference.

conditional habría   there would be
  habrían   there would be
future habrá   there will be
  habrán   there will be
imperfect había   there was
  habían   there were
present perfect ha habido   there have been
  han habido   there have been
pretérito hubo   there was
  hubieron   there were
subjunctive que haya   that there is/are
  que hayan   that there are

Hay que

When followed by an infinitive, hay que means "it is necessary to" or "one has to:"

Hay que estudiar cada día.   It’s necessary to study every day.
Hay que trabajar para triunfar en la vida.   One has to work in order to succeed in life.