[language-agnostic] What is a magic number, and why is it bad?

What about initializing a variable at the top of the class with a default value? For example:

public class SomeClass {
    private int maxRows = 15000;
    ...
    // Inside another method
    for (int i = 0; i < maxRows; i++) {
        // Do something
    }

    public void setMaxRows(int maxRows) {
        this.maxRows = maxRows;
    }

    public int getMaxRows() {
        return this.maxRows;
    }

In this case, 15000 is a magic number (according to CheckStyles). To me, setting a default value is okay. I don't want to have to do:

private static final int DEFAULT_MAX_ROWS = 15000;
private int maxRows = DEFAULT_MAX_ROWS;

Does that make it more difficult to read? I never considered this until I installed CheckStyles.