PAYE is an acronym for Pay As You Earn, and a tax system whereby your employer deducts your income tax from your pay and lodges it with the appropriate authority on your behalf.
This has the advantage that you never get your dirty little hands on the money you owe in tax, so you can't spend it and then have a large tax bill at tax time. At tax time, you have the opportunity to claim back any excess money paid on your behalf, if, for example, you have moved tax brackets during the financial year, or can claim expenses, etc.
This is the norm for full-time employees. Contractors and the like usually get paid everything they earn, then they have to declare their income and pay the appropriate amount of tax.