Boundary value analysis:

It’s widely recognized that input values at the extreme ends of input domain cause more errors in system. More application errors occur at the boundaries of input domain. ‘Boundary value analysis’ testing technique is used to identify errors at boundaries rather than finding those exist in center of input domain.
Boundary value analysis is a next part of Equivalence partitioning for designing test cases where test cases are selected at the edges of the equivalence classes.
Test cases for input box accepting numbers between 1 and 1000 using Boundary value analysis:
  1. Test cases with test data exactly as the input boundaries of input domain i.e. values 1 and 1000 in our case.
  2. Test data with values just below the extreme edges of input domains i.e. values 0 and 999.
  3. Test data with values just above the extreme edges of input domain i.e. values 2 and 1001.

Boundary value analysis is often called as a part of stress and negative testing.
Note: There is no hard-and-fast rule to test only one value from each equivalence class you created for input domains. You can select multiple valid and invalid values from each equivalence class according to your needs and previous judgments.
E.g. if you divided 1 to 1000 input values in valid data equivalence class, then you can select test case values like: 1, 11, 100, 950 etc. Same case for other test cases having invalid data classes.
This should be a very basic and simple example to understand the Boundary value analysis and Equivalence partitioning concept.