For a capacitor on a PCB, we need to look at the common formula for a parallel-plate capacitor with an area A, a distance of d between the plates, and a relative permittivity \$\varepsilon_r\$.
\$C=\varepsilon_0\varepsilon_r \frac{A}{d}\$
Let's use some common numbers: Our PCB has an area of 100 mm x 100 mm = 0.01 m2, the thickness of the core is 1.5 mm, and FR4 (a.k.a. "PCB-type epoxy") as an \$\varepsilon_r\$ of approx. 4.2. Thus,
\$C=8.85 \cdot 10^{-12} \frac{\mathrm{F}}{\mathrm{m}} \cdot 4.2 \cdot\frac{0.01\space\mathrm{m}^2}{0.0015\space\mathrm{m}}\$
\$C=248\space\mathrm{pF}\$
Even if we used a thinner dielectric (FR4 core), and maybe even a multilayer board for more than two plates, getting towards nF will be big, and we are far from getting into the µF range.
However, you can use some capacitors on the edges of your board, and distribute their voltage across the board using two copper planes acting as a capacitor. The discrete capacitors paralleled with your PCB capacitor can act as one nearly perfect lumped capacitor, giving your fast logic or power design the warm fuzzies.
You won't use a PCB capacitor if you need exact or big values, but you can use it to create a really good power distribution system on your complete design.