Degree of determinants Consider the below determinant $\triangle$:
$$ \triangle = \begin{vmatrix}
a^3&a^2&a&1\\
b^3&b^2&b&1\\
c^3&c^2&c&1\\
d^3&d^2&d&1\\
\end{vmatrix} $$
"$\triangle$ is of the sixth degree in a,b,c and d" - This is the statement given about the above determinant. 
What does "degree" of a determinant mean? and How determinant $\triangle$ is of sixth degree?

It is its degree as a polynomial in the a,b,c and d variables. In order to count this degree easier, you can look at 
$$ \triangle (x)= \begin{vmatrix}
(ax)^3&(ax)^2&ax&1\\
(bx)^3&(bx)^2&bx&1\\
(cx)^3&(cx)^2&cx&1\\
(dx)^3&(dx)^2&dx&1\\
\end{vmatrix} $$
Now you can think about polynomials only in the variable x rather than in 4 variables. If you compute the determinant, you will see that every summand is proportional to $x^6$. That is why you have of 6th degree in those 4 variables.
