This is the 803rd most frequent Japanese word.
食い
"食い" (kui) means "eating" or "consumption."
'食い' appears in the phrase '食い入るように,' which means 'intently' or 'keenly,' metaphorically derived from 'to bite into.'
その物語は本当に興味深くて、全部食い入るように読んだ。
The story was so fascinating that I read all of it keenly.
Here, '食い' refers to the act of eating and is used in a compound verb structure with '終わる' to mean 'to finish eating'.
私は朝食を急いで食い終わりました。
I quickly finished eating breakfast.
In this context, '食い' is part of the verb '食いそびれる,' which means 'to miss eating'.