Thoughts are complex things. In AI, logic is a way to simplify thoughts to their essences in a formal manner so that they can be reasoned about by machines. Like any representation, logical representations ignore some details and make a big deal out of others.
We will discuss propositional logic, and then predicate logic. But here we'll just give you a taste of what they are like.
Let's suppose you have a thought: "Ocelots are endangered." Propositional logic would represent this with a single letter, for example, "P."
Note that it ignores the fact that Ocelots are animals, that there is more than one, etc. In predicate logic, we might represent this fact like this:
Notice that in predicate logic we have more structure. This is more powerful, and in AI, this makes it slightly less efficient. In AI, there is often a tradeoff between representational power and complexity and computational efficiency.