Assets are what the business owns or is owed. Liabilities are what it owes to others.
Together with owners' equity they make up the balance sheet, and they always balance: assets equal liabilities plus equity.
Assets, by how quickly they turn into cash
Current assets are expected to become cash within a year: the bank balance, money owed by customers, inventory, prepaid costs.
Fixed assets are held and used rather than sold: vehicles, tools, equipment, property. Their recorded value falls over time through depreciation.
Intangible assets have value but no physical form: a licence, goodwill from an acquisition, a customer list.
Liabilities, by when they fall due
Current liabilities are due within a year: supplier bills, credit card balances, taxes owed, wages owed, and the portion of any loan due in the next twelve months.
Long-term liabilities fall due beyond a year, chiefly the remainder of loans and finance agreements — see debt schedule.
Why the split by timing matters
Current assets against current liabilities is what decides whether short-term obligations can be met. That comparison is working capital, and expressed as a ratio it is one of the liquidity ratios.
A business can hold substantial assets and still be unable to pay a bill, if the assets are vehicles and the bill is due on Friday.