What is the purpose of the capacitors in this circuit that are in series with this VCO?
Your terminology is incorrect but the shunt caps on the supply and tuning voltage is to provide low ESR to noise over many decades of frequency. Often the Self Resonant Freq. or SRF limits the useful RF spectrum and a smaller 1nF is needed to take over when the 10uF becomes inductive.  Hence these parts are 5 &amp; 4 decades apart in value to extend the low impedance to ripple for potentially 8 decades in bandwidth. Each source Zo(f) must be known to demonstrate precisely.

Superimposing the impedance charts may be more instructive.  There are many similar answers on this site if you search; Shunt caps, SRF.

It often extremely important to remove all ripple noise V to reduce phase noise on the VCO.  However if were used in a PLL where negative feedback requires more bandwidth to track a lower noise XO &amp; phase detector, then the Vtune caps may be smaller.