The cross product of two vectors produces a vector that is perpendicular to the plane the input vectors lie on and whose length is equal to the area of the parallelogram formed between the two vectors. For example, the cross product of two vectors that lie in the plane produces a vertical vector like this.
The order you multiply the vectors matters. If we change the order of the cross product we get a vector with the same length and pointing in the opposite direction.
In general, the cross product of two vectors and is given by this formula.