"Can't," "I can't," or "#can't" is a popular line (and tag) on Tumblr that is used to portray that the person posting cannot handle the things they are seeing.
It is a cousin of the "what is this, I don't even" line, but while that is used to portray how completely baffled someone is at the amount of stupidity being thrown at them, "can't" usually (though not always) has a positive connotation, relating specifically to things that are so funny, ridiculous, or awesome that the poster simply cannot properly react.
Like the "what is this, I don't even" line, "can't" is not meant to be grammatically correct. Can't is intentionally over the top and silly. The lack of grammar (and often punctuation) is meant to convey emphasis on the word being an off-the-cuff, knee-jerk reaction to whatever is being presented. Reasons for having your brain break to the point of "can't" include receiving a supreme compliment from someone you admire, seeing some awesome art or trailers for a movie you like, or basically anything else that makes you unable to type complete, structurally sound sentences.
The "can't" is usually portrayed visually via someone falling over.
Examples of CAN'T reaction gifs: Hook can't, Godzilla can't, this washingmachine can't, Bilbo Baggins can't, and I guess it runs inthe family, because Frodo can't either.