As with many things, the end quality depends on the weakest link. Because most cameras are quite good, even cheap ones (even from mobile phones), the weakest link is mostly the person behind the camera.

When learning some theory and practice, photographers can work around some pitfalls of cameras, but also knowing the shortcomings of a camera. When that knowledge is gained, than it is time to step up.

I have seen photographers making beautiful pictures with a phone, and I have seen people making crappy pictures with some high end consumer camera.

So if you ask specifically about important, you can take the following items into account:

• If you want to print the picture in a large format, you need more pixels, thus more quality. (See J's comment below, if viewers are at bigger distance, you need less pixels).
• If you are satisfied with the pictures you make, you do not need a new camera.
• If you enjoy your hobby more occasionally buying something new, then maybe the quality of the camera is not important, but to make your hobby nicer (so it's important to enjoy your hobby more).
• If you are a professional, then it depends on the context you need the camera for (e.g. what working conditions, high ISO needs, shutter speeds for lenses, video quality, sensor size to print large pictures etc). But if you are a pro, you probably (hopefully) know when the quality of a camera is the bottleneck.