A good camera is one that does what you need it to do. It is that simple, in a sense. There are a lot of things that go into making good pictures, and all of them are important. The capabilities and mechanics of the camera matter, but of equal importance are environmental conditions and the skill of the user. The quality of the optics in the lens actually matters more than the camera itself.
When pixels matter
Some camera makers make a big deal out of pixels. More pixels must make a better camera, right? No, not really. Pixels are just one aspect. They are important, but pixels do not make the camera. Pixels are like tiny buckets on the light sensor inside the camera that capture light, and the light in those buckets become a photograph. Pixels are measured in the millions, which is why they are called megapixels.
The more megapixels you have, the bigger the photograph can be, but that is all it means. An image that is poor to start with will only get worse as the size goes up. When you make paper pictures, or prints, the pixels will matter more. In reality, a one-megapixel picture is all you need if you are just going to email or post on Facebook. An 8 x 10 print needs about seven megapixels.
When camera size matters
The size of the camera matters more, really, because the light sensor is what actually takes the information in that will become a photograph. A bigger and more sensitive light sensor will make a better picture. Phone makers are now able to pack millions of pixels onto a tiny light sensor, but that same number of pixels inside a DSLR (Digital Single Lens Reflex) professional level camera will make a much better picture because it has a much larger sensor.
There is no single aspect that makes one camera better than another one. You get what you pay for in cameras, but at the same time, if you don't need the higher level of camera, there is no real point in spending more. The most important thing is to figure out why you want a camera and what you intend to do with it, and then find the camera that best fits that criteria.
What you need
If you want to post pictures on social media sites, send photos to friends via email, and just enjoy basic shots on your computer, you can probably get by with the camera on your phone.
If you want to take casual photos, but want a little more control and quality, a point-and-shoot will work fine. This type of camera has more optics and more power, and everything is all set to make pictures, so you can just point and shoot. These usually have some zoom lens capability as well. There is a little creative control available, but not much.
The top level, which is what serious amateurs and professionals use, is a DSLR, which has interchangeable lenses. You have total control with this type of camera and can make professional quality photographs. There are levels within this category — beginner, intermediate and advanced. Purists calls these "real" cameras, and they are for when you want to take photography seriously as a hobby or profession.