Abbreviation of コネクション. Refers to personal connections or influence used to gain an advantage, often in job hunting or business.
See also: コネクション
彼はコネでその会社に入ったらしい。
It seems he got into that company through connections.
Without connections, you can't find a job in this industry.
He got into that company by using his father's connections.
People who have connections in that industry find it easier to get jobs.
It's said that she was hired through connections.