This fixture is not wired per code, you should have only one white wire for each colored wire, you should never have only one colored wire and more than one white wire.
What the previous posters are suspecting is you have a three-way circuit so that two or more switches can control the fixture.
You can use a multi-tester of test light to see if you have current between the black wire and one of the white wires when the switch is turned on. If you have current through more than one white wire then stop and call an electrician. You might inadvertently overload a neutral. If your switch does not read on and off then you probably have a three-way circuit and you may need an electrician to sort it out.