Attribute-based access control (ABAC) is a way to give people access to certain things in a secure and organized way. Think of it like a giant game of dress up. If you have the right items of clothing, the game's rules say that you can come in and play.
In ABAC, those items of clothing are called "attributes". For example, attributes could be things like a certain age, specific job duties, or certain titles. All these attributes can be part of someone's "profile." When someone wants to access a website, they present their profile to the game (the website). The website looks at the person's profile and checks to see if they have the right attributes. If they do, the website gives them permission to enter; if they don't, it doesn't.
So, ABAC is a system for giving people access to things, like websites, based on their attributes. It is secure because it only allows access to people who have the correct attributes, and it is organized because it is designed to do this in a consistent way.