To add to Ohm's answer
A class is a description of a "thing"
An instance (or object if you prefer) is an actual thing.
Using a car as an example
A description of a car might be model, make, engine, fuel consumption, fuel type, top speed, registration number etc...
A description applies to all cars but an instance of a car applies only to one specific car
You might "buy" a car. You can't ask an instance of a car to buy itself as it doesn't exist yet, you have to create a car from a car class to get an instance (@car = Car.new)
the "new" method has to be a class method simply because the car hasn't yet been made. (What you you do @car = what???. @carsomething?) The "new" method needs to make the car for you and hand it over for you to do what you want with it within the bounds of the classes restrictions
But the car hasn't yet been saved and you have the job of describing what the car should be so you could give the make a value of "Ford" and the model a value of "Mondeo" and fill the rest of fields.
These are all properties of a Car class.
Now you can tell @car to do something like start up, you can find out how fast the car is travelling, what color it is, etc... It's no good asking a Car class what colour it is as the class doesn't know but you should be able to ask the Car class what colours are allowed and get a list back so you can choose the colour you want when you are creating it. Of course the Car class should reject invalid values before being saved.
Once saved you can get that instance anytime you like, you can determine how old it is simply by comparing the current date with the date it was created, you could create a class method that gets all cars over a certain age but it's no good asking @car (the instance) to get you a list of cars, why on earth should your Ford Mondeo need to know anything about other ford Mondeos' there are tens of thousands of them on the road.
In other words the distinction between a class and an instance is just that. There are things you can do with an instance that it doesn't make sense to do on a class and vica versa.
A Ford Mondeo might come in different colours, engine sizes etc...
These are all related to a car's class
You might own a ford mondeo and the mondeo you own would be an instance of the car class