dedication
Explanation
The comic shows a shirtless man with his eyes closed, speaking from what appears to be an intimate setting. He says: "I'd like to dedicate this oral sex to world peace."
The caption below reads: "Our relationship declined sharply once I discovered you can dedicate anything to anything."
The joke is about the absurdity of applying the concept of "dedication" to inappropriate contexts. Dedications are a social convention typically reserved for creative works, performances, athletic achievements, or other public accomplishments ("I'd like to dedicate this song to..." or "This book is dedicated to..."). The character has discovered that the linguistic formula of dedication has no inherent restrictions on what can be dedicated or to what cause, and has begun applying it to sexual acts.
The humor comes from the incongruity between the solemnity and formality of a dedication (usually a public, earnest gesture) and the private, physical act it is being attached to. The man treats the oral sex as if it were a concert performance or an Olympic medal, dedicating it to a grand cause like world peace, which is both absurd and pretentious.
The caption reveals the partner's perspective: the relationship deteriorated because this person's discovery that "you can dedicate anything to anything" led to a persistent, annoying habit of making grandiose dedications of mundane or private activities. The implication is that this is not a one-time joke but an ongoing behavior.
The hover text ("Before you say anything, I'd like to dedicate this breakup conversation to pioneering portraitist Frida Kahlo") extends the joke to its logical conclusion: even the breakup that results from this annoying behavior itself gets a dedication, showing the character has learned nothing and will dedicate absolutely everything to something.