Direct Answer to Your Question
Pronouns are words that substitute for nouns. In the case of ¿Como te llamas?, you are using what is alternatively called a pronominal verb or a reflexive verb and these require reflexive pronouns such as me, te, se, nos, and os. At an elementary level you will use these verbs in two main contexts.
- Actions where the person doing the action also receives the action: "I wash myself" is (yo) me lavo. We may not always say it exactly like this in English, but it still makes intuitive sense. Many morning routing activities (because you do them to yourself) fall in this category: "I brush my teeth" is (yo) me cepillo los dientes and "I shave myself" is (yo) me afeito.
- Phrases like ¿Como te llamas? which don't make much sense right now. I honestly wouldn't worry too much about the grammar here, but rather focus on the pattern and respond Me llamo Stanford.
We often focus too much on the mechanics of grammar. It's valuable to know when to focus on the grammar and when to use your intuition and forget about grammar. For now, I'd recommend focusing on the grammar for #1 above and not so much for #2.
Pronouns at an Elementary Level
Yo, tu, vos, él, ella, usted, nosotros, vosotros, and ustedes are personal pronouns used in the subject of a sentence. In an elementary Spanish class, you will see these the most.
Sometimes, the pronoun is an object instead of a subject. "Will you help me?" can be asked in Spanish "¿(Tu) me ayudas?" In this case, the person asking the question is the object because he receives the action (help). Me is a direct object pronoun along with te, lo, la, nos, os, los, and las.
Probably the best summary of Spanish pronouns is available from an old course at Indiana University - Purdue University Ft. Wayne.