The determination of the amount of tax any individual or company is liable to pay. This may be done in one of two ways. One is that the taxpayers make tax returns, listing their income from various sources and any facts affecting their entitlement to tax allowances. The tax authorities then make the actual assessment. The alternative method is self-assessment: besides supplying information on their income and entitlement to allowances, taxpayers produce their own assessments, applying the tax rules to their own figures; these self-assessments are then checked by the tax authorities. In the UK the assessment is made by an Inspector of Taxes if a tax return is made within a time limit; after this taxpayers have to produce a self-assessment. Self-assessment applies to all individuals liable to income tax in the US.
Reference: Oxford Press Dictonary of Economics, 5th edt.