A continuous quantity is a quantity that can take any value within one or several intervals. In other words, continuous quantities can be measured to any arbitrarily high degree of precision. Consider a person's age.
The age of a person is changing constantly, depending on how precisely it is measured. Counting only in years, a person could be or years old. Counting more precisely, he or she could be and a half, years and months, or even years and days old.
If the input of a function is a continuous quantity, the function is said to have a continuous domain. The graph of such a function is typically a curve or a line.
Continuous quantities commonly include length, weight, volume, and difference in time, such as the volume of liquid in a drinking glass or the time that has passed since a person's last haircut.