To "text someone" means to send them a text message on a mobile phone. A "text message" is like email but shorter and can be sent to the person's phone number instead of to an email address.
This is a phrase that has only started to be used this way in the last 5 years or so. Before that, the word "text" was only a noun. But now, "text me" is a common phrase for people who use mobile phones.