It's a mix of:
* "Vek": meaning "awake" or "alert"
* "Klempt": meaning "clogged" or "stuck"
So, it literally means "clogged up with emotion."
Think of it as a feeling of:
* Choked up: You can't get the words out.
* Emotionally paralyzed: You can't think straight or take action.
* Overwhelmed by joy, sadness, or any other strong emotion: You're flooded with feeling.
The word "veklempt" often implies a feeling of:
* Tenderness: A deep, sentimental emotion.
* Nostalgia: A longing for the past.
* Awe: A sense of wonder or amazement.
While it's a Yiddish word, "veklempt" has become increasingly common in English, particularly in the United States.