The preposition is an invariable part of the sentence that establishes a relation between two words. They don't have a meaning of their own and show position, time, relationship, etc. between words.

Examples of the construction
preposition + infinitive are shown below:

Ella sigue sin mirar atrás.
She keeps going without looking back.

Él salió sin decir adiós.
He left without saying goodbye.

Yo tengo un boleto para viajar.
I have a ticket to travel.

Yo camino al restaurante para cenar.
I walk to the restaurant to have dinner.

Tomamos café después de cenar.
We drank coffe after having dinner.

Yo solía ir a correr todas las mañanas.
I used to go jogging every morning.