The c is a constant (fixed number) that we don't know but it helps point to the y intercept. Let's say that c = 10. If that was the case, then
y = x^2+5x+c
turns into
y = x^2+5x+10
Now plug in x = 0. Note how y turns into...
y = x^2+5x+10
y = (0)^2+5(0)+10
y = 0+0+10
y = 10
Which means (0,10) is on this parabola. This is the y intercept because x = 0. In general, the y intercept of y = x^2+5x+c is the point (0,c), where c is a placeholder for some fixed number.
