OpSec is short for Operational Security. Operational Security is the process of identifying mission/operation critical information that may be the target of an adversary in order to disrupt your operations. The goal is to protect and secure the information to prevent an adversary from being able to obtain it. In terms of anonymity, this can be described as a process to prevent an attacker from being able to successfully gain the information necessary to deanonymize you and/or disrupt your operations.
If you want to remain anonymous, you need some form of OpSec to prevent most techniques and mistakes used to deanonymize someone. Remember, there is no such thing as 100% anonymity or 100% security, the best you can do is be reasonably secure against attacks and techniques that may be used by your adversary.
Maintaining good OpSec will ensure that you remain anonymous, and your operations continue smoothly by using a structured and efficient approach to security. OpSec may look scary on paper, but it is actually very simple. There have probably been numerous times when you have actually used OpSec without even realizing it.
First you need to have a threat model, this threat model can be super simple and abstract or super simple and structured using something like Attack Trees or STRIDE, it is completely up to you. The basic requirements here are that you know what you are tying to protect and who your adversary is. From this point, you can study and learn about your adversary, including what attacks and techniques are they going to try in order to get to what you are trying to protect. From this point you can find mitigations and countermeasures in order to slow down or stop your adversary entirely, keeping what you are trying to protect safe.
In the context of anonymity, what you are trying to protect is most likely going to be your true identity. However, this may vary from person to person depending on the situation.