Sometimes an attribute should be worked out when it's read, or checked when it's set. A property looks like a plain attribute to the code using it, but runs a method behind the scenes:

class Temperature:
    def __init__(self, celsius):
        self.celsius = celsius

    @property
    def fahrenheit(self):
        return self.celsius * 9 / 5 + 32

    @fahrenheit.setter
    def fahrenheit(self, value):
        self.celsius = (value - 32) * 5 / 9

t = Temperature(100)
print(t.fahrenheit)
t.fahrenheit = 32
print(t.celsius)

t.fahrenheit has no brackets: it reads like an attribute. Only one number is stored, so the Celsius and Fahrenheit values can never disagree.

A setter is also the place to enforce rules. By convention, a name starting with an underscore means "for this class's own use", so code outside uses the property instead:

class Person:
    def __init__(self, name, age):
        self.name = name
        self.age = age

    @property
    def age(self):
        return self._age

    @age.setter
    def age(self, value):
        if value < 0:
            raise ValueError("age can't be negative")
        self._age = value

p = Person("Ada", 36)
p.age = 37
print(p.age)
try:
    p.age = -1
except ValueError as e:
    print("Refused:", e)

self.age = age in __init__ goes through the setter too, so even a brand new Person can't start with a negative age.