It's a combination of the preposition "con" (with) and the pronoun "tigo" (you, informal).
Here are some examples:
* Quiero ir al cine contigo. (I want to go to the movies with you.)
* Estoy feliz de estar contigo. (I am happy to be with you.)
* Voy a la playa contigo mañana. (I am going to the beach with you tomorrow.)