I found this hypothetical conversation on the internet. It is an attempt at making fun of people who are members of the "baby boomer" generation, which is the generation of people who were born immediately after the end of World War 2.
Millenials: Ok, boomer.
Boomers: This is Illegal Discrimination.
The word "Snowflake" is an insult that indicates that the person is overly convinced of their individuality and that they also are easily offended. It has been used as an insulting generational title for the generation more commonly described as millenials.
The phrase "Ok boomer" is a phrase used by people younger than baby boomers to point out the age of a baby boomer and then sarcastically disagree with them in a dismissive way.
The entire exchange, when taken together is an attempt at pointing out that when one generation uses a pejorative title for another generation and then is unwilling to have one used in response, the first generation is acting hypocritically.
The humor here centers around the boomer's response - declaring that the phrase "Ok, boomer" is illegal discrimination immediately after using a similar insult is hypocritical. Pointing out hypocrisy in others is insulting, and insults are generally considered humorous.