What is Lagrangian, dual problem?

For minimising $f(x)$ subject to $g_i(x) \le 0$ and $Ax = b$, the Lagrangian is $L(x, \lambda, \nu) = f(x) + \sum_i\lambda_ig_i(x) + \nu^\top(Ax - b)$, and the dual function is $d(\lambda, \nu) = \inf_xL(x, \lambda, \nu)$. The dual problem maximises $d$ over $\lambda \ge 0$.