please explain the marked step

Dear student, 

The marked expression is the discriminant of the equation $x^2+x+\lambda =0$.
For inequality 
$$\begin{gathered} x^2+x+\lambda \ge 0 to hold for exery real x, we must have \\ discriminant\le 0 \\ i.e. 1-4\lambda \le 0 \end{gathered}$$

Hope this information will clear your doubts about topic.

Regards