A bid price is the highest price that a buyer (i.e., bidder) is willing to pay for a good. It is usually referred to simply as the "bid".
An unsolicited bid or purchase offer is when a person or company receives a bid even though they are not looking to sell.
A bidding war is said to occur when a large number of bids are placed in rapid succession by two or more entities, especially when the price paid is much greater than the ask price, or greater than the first bid in the case of unsolicited bidding.
In other words, bidding war is a situation where two or more buyers are so interested in an item (such as a house or a business) that they make increasingly higher offers of the price they are willing to pay to try to become the new owner of the item. 
In the markets
In the context of stock trading on a stock exchange, the bid price is the highest price a buyer of a stock is willing to pay for a share of that given stock. The bid price displayed in most quote services is the highest bid price in the market. The ask or offer price on the other hand is the lowest price a seller of a particular stock is willing to sell a share of that given stock. The ask or offer price displayed is the lowest ask/offer price in the market (Stock market).
- bidding war in investopedia, http://www.investopedia.com/terms/b/bidding-war.asp investopedia
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