PostgreSQL is a SQL-type database system. It has been around for a while, and is in the middle of a sort of revival. Installing Postgres on your own system can be a little difficult. Last time I tried, I was helped through the process while doing the Udacity Intro to Programming Nanodegree.
Recently I had to reinstall Postgres, and there were some useful improvements to the process when guided through it in my Dataquest lessons.
Postgres.app is an application you can install on your Mac which simplifies a lot of the legwork, particularly when setting up new databases, servers and so on.
When you want to install a commonly used Python library for interfacing with Postgres, psycopg2 is a good option. You can do this easily with Anaconda:
conda install psycopg2