The "adj" abbreviation is a common way to indicate that a word is an adjective. It stands for "adjective."
Here's an example of how you might see this:
* cynical adj. (of a person or their attitude) believing that people are motivated by selfishness and that nothing is good or sincere.
This tells you that "cynical" describes a person or their attitude, and that it is a word used to characterize someone who believes that people are motivated by selfish reasons.