The process of selling assets for cash.
This situation generally arises when a company can no longer carry out it's business as intended, by making profits and, share holders do not have any chance of gaining from investing in the company.
The cash generated out of liquidation is usually spent on reducing debts that company own to its lenders.
For example, Lehman Brothers filed for Chapter 11 bankruptcy protection on September 15, 2008 and now in Jan 2009, Barclay's [which took over Lehman, LEHMQ:US] is in the process of liquidating it, though Lehman has a couple of trillion dollars in assets.
Winding up would mean liquidating the assets of a corporation or partnership, settling accounts, paying bills, distributing remaining assets to shareholders or partners, and then dissolving the business. Winding up a non-profit corporation requires a plan for distribution of assets to some charitable or other non-profit entity. 
Liquidation is the conversion of assets into cash by an Investor getting rid of a position in a particular type of security.  When Investors convert assets into cash for there own personal accounts, they may have no reason too convert, and may spend the proceeds on whatever they want, whenever they want.
Liquidation is simply the conversion of assets into cash, liquidity refers to how quickly you can convert your assets into cash.  For example, a portfolio manager might decide to liquidate a position in a stock by selling all the shares of that stock held in the portfolio. 
c.1575, "to reduce to order, to set out clearly," sense of "clear away" (a debt) first recorded 1755. The meaning "wipe out, kill" is from 1924.