The order of liquidity plays a part in the balance sheet by determining which assets are listed first. This order determines which are more useful on an immediate basis.
The order of liquidity is an already determined listing procedure for listing assets on a balance sheet. Liquidity, in this purpose, generally means "the closest to cash," meaning the quicker the asset can be turned into real cash to be used. The list begins with the closest one to turn into cash (generally the actual cash account) and goes down from that account.
In a current assets section, there will usually be four (maybe five) accounts, depending on the business. Right after cash would be "marketable securities," which means things that can be sold in a short amount of time for cash. After this would be the "accounts receivable" account, since this can be liquidated according to the company's credit terms. The last account in this section should be the "inventory" account, since making cash off of the inventory can take weeks or months, and sometimes may require a significant discount in order to clear goods faster.
As well as having current assets, there are "intermediate" assets and "long-term" assets. Intermediate assets would include vehicles for a company, and long-term would include buildings or land for the company.