feel – noun C, usu pl
I almost can't handle all the feels I get these days.
This is a game that punches you right in the feels.
His story made me feel some feels and think some thinks, and that's worth something.
It wasn't a full out emotional attachment but it was enough to get the feels flowing.
The noun feel is not new – it's been around since the fifteenth century – but recently it has been used in a new way, mainly on social media. While the traditional senses are singular, the new use is countable and often plural.
Feels are intense feelings or emotions, especially in response to a work of art such as a book, film, or even a game, as in the second example above. That example is interesting for another reason: it suggests that feels are located somewhere in the body, probably the abdomen, so that when they are particularly intense you feel as if you have been hit there. The association between feelings and this area of the body is deeply rooted in the language: we talk about gut feelings or reactions, or say that someone has fire in their belly, or that your stomach churns when you are scared or excited.
The popular abbreviation TFW, or That feel when... is used to introduce an idea or experience you think people will relate to. Like the plural use of feels, it presupposes a common set of reactions, whether to art or life, that requires no further explanation or analysis. The truncation of the noun is also characteristic of the language of the internet and social media in particular.
The social media use of feel is short for feeling. It was probably first used online in 2010 in the caption I know that feel bro to a drawing of two men embracing.