Learn Russian: Это крупная компания.

While большая means big in a general or physical sense, крупная (from крупный) is used for scale, importance, or financial magnitude. You will frequently see крупный used with businesses, sums of money, and projects to mean major or large-scale.

Since компания is feminine, why does the sentence start with the neuter это instead of эта?

Here, это is acting as a fixed pronoun meaning 'This is', which stays neuter regardless of the noun that follows. If you wanted to say 'this large company' as a phrase (without the implied 'is'), you would use the feminine matching form: эта крупная компания.

Does компания mean a group of friends or a business?

It can mean both, just like in English! It is used for a commercial enterprise (a business company) and a social group (a company of friends). Note that it sounds exactly like кампания, which means a campaign, but they are spelled differently.