If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30th day as well. A conjecture is an educated guess that is bases on known information.
If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.
This method to use a number of examples to arrive at a plausible generalization or prediction could also be called inductive reasoning.
If our conjecture would turn out to be false it is called a counterexample.
Make a conjecture for the following figure