'Risk weighted assets' means the assets in a bank's balance sheet, but adjusted for risk.
Banks have minimum capital requirements (mostly equity) that they have to hold in order to be safe. If you just required a bank to hold capital equal to a fixed proportion of the assets in its balance sheet, then it would take no account of the different risk levels of different assets in that balance sheet.
By weighting the assets by risk level, you can ensure that a bank which holds more risky loans is required to hold more capital to keep it safe.
