Emotions are the physical response to a stimuli while feelings are the mental association or reaction to that physical state.
Emotions are considered as our bodies’ responses to external stimuli and feelings are mental associations and reactions to these emotions. The main difference between emotions and feelings is that emotions are physical states whereas feelings are mental associations.
A feeling originates from the brain and are very similar to thoughts.
The terms emotion and feeling are often used interchangeably in vernacular. Typically, when people talk about their emotions, they are talking about their feelings associated with an emotion.
Our emotional responses can sometimes get a bad rap. Historically, popular culture tends to regard emotions as something of a messy human characteristic that should be avoided (see Spoc in Star Trek who is logical: avoiding emotions rather than feeling them).
Emotions, however, have many evolutionary advantages and the zeitgeist is shifting on this topic. If one can understand how their emotions affect them, they can mitigate the negative effects and enjoy the positive effects.