What is a "TV-L 13" position?
TV-L is the German public servant remuneration grade table (Tarifvertrag für den Öffentlichen Dienst der Länder (TV-L)). It is how civil servants Germany are graded for their salaries and similar conditions for their work.

Depending on where your position is, you'll be under TV-L West, or East, or Berlin, or Hessen. Something in your letter might specify this. Either way, there is information on the details at the Öffentlicher Dienst website.

Assuming you'd be in West Germany, taxed as a single (i.e., not married or living with a life partner or children), this boils down to a basic salary of €2103/month with a net salary after all taxes and health insurance payments of €1383/month.

This will increase as you remain hired, you'll go up the staircase of salaries, going from 1 to 2 after 1 year, from 2 to 3 after an additional 2 years, etc. Each step is a monthly salary increase of about €150/month net.