SQL Select Statement with WHERE, AND, OR

The way you use parentheses in the description of your goal is correct. The syntax is:

SELECT name, sex, fur, color 
    FROM dogs 
    WHERE sex="male" AND fur="short" AND (color="black" OR size="big");

According to Operator precedence for MySQL AND has higher precedence than OR.

So C1 AND C2 OR C3 will be treated as (C1 AND C2) OR C3

To override the default precedence you need to use parenthesis as:C1 AND (C2 OR C3)

In your case the right query is:

SELECT name, sex, fur, color 
FROM dogs 
WHERE sex='male' AND fur='short' AND (color='black' OR size="big");

Make sure to add parentheses, so the OR condition gets evaluated correctly.

SELECT name, sex, fur, color 
FROM dogs 
WHERE sex='male' AND fur='short' AND (color='black' OR size='big');