Quick explanation:
The verb "to know" is translated to Spanish as saber and conocer. In Spanish, both saber and conocer have different meanings. Let's see a few examples of both:

Conozco a pocas personas aquí.
I know a few people here.
Tú conoces a mi primo.
You know my cousin.
Nosotras sabemos la lección.
We know the lesson.
Recién tiene un año y no sabe hablar todavía.
He just turned one year old and he can't speak yet.

We will review in detail the difference between conocer and saber in the long explanation.

Long explanation:

CONOCER

*when we know or when we have met a person.

Tú conoces a mi tía Berta.
You know my aunt Berta.

Mis amigas conocieron a mi novio ayer.
My friends met my boyfriend yesterday.

Vosotros no conocéis a mi familia.
You all don't know my family.

*when we have been somewhere (town, city, etc).

¿Conoces Perú?
Have you been to Peru?

Yo conozco la salida a la Calle Central.
I know the exit to Central Street.

¡No puedo creer que no conoces Acapulco!.
I can't believe you haven't been to Acapulco!

*when we are familiar with a place, thing or a concept.

¿Conoces la leyenda del "Jinete sin Cabeza"?
Do you know the legend of "Sleepy Hollow"?

Él conoce el estadio donde es el partido.
He knows the stadium where the match is taking place.

La psicóloga conoce ese tipo de actitud.
The Psychologist knows that kind of behavior.

SABER

*when we know certain facts or information.

¿Sabes las reglas del básquetbol?
Do you know the basketball rules?

Yo sé cuales son sus intenciones.
I know what his intentions are.

Los niños ya saben las tablas de multiplicar.
The children already know the multiplication tables.

*when we memorize something or know it by heart.

¿Se saben los estudiantes el juramento a la bandera?
Do the students know the pledge of allegiance?

Ella sabe de memoria el poema que su esposo le escribió.
She knows by heart the poem her husband wrote to her.

Mi secretaria sabe la clave de mi tarjeta de débito.
My secretary knows my debit card pin number.

*when we know how to do something.

¿Sabes montar a caballo?
Do you know how to ride a horse?

Mercedes, mi empleada, sabe cocinar delicioso.
Mercedes, my maid, knows how to cook really well.

Estoy feliz porque ya sé hablar español!
I am happy because I now know Spanish!