(countable) A company is an organization for doing work for money.
He works for a big company.
I own this company, so it's a problem for me if people don't buy what we make.
(uncountable) Company is people who are visiting other people; people who are in other peoples' house so that they can talk to the other people, or people who are walking with other people or being somewhere with other people.
I can't talk to you on the phone right now, because I have company. (people in the house.)
(uncountable) When someone keeps someone else company, they stay with the person.
Will you keep me company while I go to mail this letter?