If I were Dr. Seuss, I would simply begin: "What does it mean / When I look at the screen / at a show or a meme / and I say 'I feel seen'?" I know what it means when someone says they feel heard--they feel like someone has really listened to them, as if their words have been paid attention to. I know what it means when someone says they feel touched--they feel like someone has made a connection with them on an emotional level, as if physical contact were happening in the soul. In both cases, the primary senses have been abstracted to their essential emotional experience.
We don't feel seen the way we feel happy or sad because seen isn't exactly an emotion; it's a passive verb. In English, we feel passive verbs all the time: I feel exhausted; I feel prepared; I feel disrespected. We know the feelings associated with having those verbs happen to us, so we can easily translate the action into the realm of emotion (weariness, accomplishment, embarrassment). It helps that these verbs also describe instinctually emotional experiences. It would be hard to imagine feeling babysat, or grocery-shopped, or deplaned.
So what does being seen feel like? I don't think we mean seen as in "viewed." I can't imagine someone receiving a relatable meme from a friend and responding, "I feel famous." It's also not seen as in "watched." We're not smashing that "Like" button and laughing because the government is watching us through our front-facing iPhone cameras. It's more like "I feel understood" or "I feel affirmed" or "I feel recognized." It's a feeling of identification with the content that has truthfully reflected our own experience back to us, like Narcissus, staring at his own image in the lake, feeling so seen right now.
But to feel seen isn't simply narcissism. The creator of the meme account, the friend who sent you the post, the other accounts who have liked it ... to feel seen is to find comfort in the shared recognition of one's own experience. When you feel seen by a relatable meme about, say, work sucking, and a bunch of others feel seen by it too, that makes the experience of work sucking that much less lonely. You recognize yourself and laugh, realizing you're not alone. You're in a community of Narcissi, all staring into the same puddle and gleefully shouting, "That's me!" But a Monday-level clue needs to cut right to the core of the feeling: "I feel ___" (comment about something relatable).