An acquisition is an action by a corporation to assume control of a target firm. This is done by buying either all or most of the target's ownership stakes. Acquisitions can either be friendly (the target firm agrees to be acquired) or hostile (the target firm does not agree and the acquirer has to buy large amounts of the target to assume control).
Typically acquisitions are undertaken in order to expand into a new sector or to grow within the sector. For example, if a technology firm has a key supplier for an essential part, they may decide to acquire the supplier both to ensure a consistent supply of parts and to reduce the amount available to competitors.
The acquiring company will usually offer a premium to the target company (the difference between the acquisition value and the market value of the target) in order to provide incentive to the existing shareholders to sell and this premium will often be roughly equal to the value of intangible assets and goodwill in the target company.