Minority interest is an amount NOT owned/entitled to by a consolidating entity. An example with clarify.
Company A acquires 95% of company B's stock and by GAAP accounting rules company A must consolidate (all/completely) company B's financial results into its own. But remember, there is still 5% of company B that is not owned by company A. The way this is treated is by "backing out" this 5% with the line item Minority Interest.
So the overall procedure is for A to consolidate all of B's financial results (revenue, COGS, SGA, etc..) but then BACK OUT the portion of B's earnings stream (the 5%) that it does not own. This is minority interest on the income statement. The balance sheet follows a similar logic and minority interest is treated the same way - as a liability - the portion of consolidated assets that it does not own.