Anonymous has many definitions.
You can consider yourself anonymous online if you don't use your real name to post, however, your traceable ip address is always visible to the website you connect to. You can help to hide this location by using the internet from a coffee shop, work, or other public area, however, these places would still be able to determine your identity.
In order to achieve truly anonymous internet connections, you need to research software such as VPN, TOR, or Tails depending on just how anonymous you strive to be. Just be prepared to trade speed and convienence for anonymity.
The collective group of people claiming to belong to anonymous are members of decentralized groups of individuals with common morals, ethics, and goals. We are all anonymous in this sense and the level of activity within the groups defines your level of commitment to the collective (to yourself).
You can be sure that members of the Anonymous collective are certainly familiar with the software mentioned above.