It's a Filipino slang term (literally "to pull out) for expressing feelings (usually love), creating a "deep meaning" to it.
It's roughly
equivalent that you usually find in r/im14andthisisdeep.
When you hear a very
emotional or romantic song and you start tearing up because you remember memories of your ex, the song is said to be hugot.
When someone tells a story and you react strongly to it because you have similar experiences and start crying, the story is said to be hugot.
It is only said in a joking manner though. It’s a way to blunt the impact somewhat.
It can be very cringe sometimes that can make
your soul come out of your body.