An assertion is just a statement of something that should always be true. For example 1==1 ought always to be true, right? You mainly use assertions when you're developing or testing code. So, if you'd expect a variable to be equal to 5, you assert myVar==5; If it isn't equal to 5, the program will explode or the test will fail - letting you know that your expectation was wrong and the code was doing something different.
I hope that sort of answers your question.
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