A bear hug is an acquisition strategy where the acquirer makes an offer to buy the shares of the target company at a price that is clearly higher than what the target is currently worth. This offer is intended to eliminate the possibility of competing bids, while making it difficult for a target company to reject the offer.
The board of directors of the target company has a fiduciary responsibility to obtain the best possible return for the shareholders of the target business, so the board may essentially be forced to acquiesce and accept the offer. Otherwise, the board may face lawsuits from shareholders. Another advantage of the bear hug is that other potential bidders will very likely stay away, since the price offered is so high that it would be uneconomical for them to top the offer.
If the board does not accept the bear hug offer, there is an implied threat that the acquirer will then take the issue directly to the shareholders with a tender offer to purchase their shares. Thus, the bear hug is essentially a two-step strategy: an initial overwhelming offer to the board, followed by the same offer to the shareholders.
While there is a good chance that a bear hug strategy will work, the downside is that it can be extremely expensive, so the acquirer has little chance of earning an adequate return on its investment in the target. This approach is only needed for a hostile takeover, since a friendly one can usually be achieved with a smaller investment.