What is Capacitive Loading (Intuitive understanding)

But what does it mean when one says,"It is a capacitive load"

It means the load behaves like a capacitor. You have to deliver charge to it before the voltage across it will change.

why output impedance should be low for capacitive loads?

Because if you want to change the voltage across this load, you'll have to deliver a significant current. You need a low-impedance load to deliver a current without the voltage sagging.

This is just a conceptual model, and won't hold up to much scrutiny, but might help get your mind going in the right direction.

Imagine your circuit is a piece of tubing. The power source is you blowing into one end. DC could be you blowing with a steady pressure, while AC could be you blowing in and out.

Now, cap the other end and put a tiny hole in it...a restriction if you will. This is a resistive load. Constant pressure = constant flow.

For the capacitive load, imagine replacing the small hole with a balloon instead. Now constant pressure does not equal constant flow. The flow slows down as the balloon/capacitance "fills up".

Simple answer

Big Capacitors store charges like a tiny battery. They draw more current with the rate of change of voltage, just as shock absorbers react with more force with pot-hole step size or rate of change of position = speed. Current is a good analogy to force as it is proportional to torque in motors. So Capacitive loading is like choosing bigger shocks for a heavier vehicle to create a greater force to slow down the axle over a bump. A washboard road creates an AC force on the axel and the shocks must be selected to match the spring-mass resonance for best damping.

Ticky tacky technical answer

All Capacitors have some Effective Series Resistance, ESR, therefore creating the minimum possible resistance at some breakpoint frequency. Then they become inductive above this.

Power supplies using negative feedback have limited gain-bandwidth products so the output impedance is reduced by this gain. Thus as load frequency increases this output impedance is the opposite of a low ESR shunt capacitor.

Often the bandwidth of acceptable low impedance of a cap spans only a few decades for low impedance, and ESR also changes with bulk size and chemistry of the cap. Therefore in critical SMPS applications it may be common to see a range of output Caps from Ceramic, Film to Electrolytic.

The impedance of a cap is defined as \$\dfrac {1}{\omega C}+ESR\$ up to the breakpoint frequency where these are equal.

Thus when paired with an active LDO or SMPS that a rising low impedance defined from the load regulation error and up, the goal is to achieve a near flat output impedance, yet often never achieved due to complexity and tolerance errors.

Load regulation error for some load impedance is like any impedance divider as a ratio of load to total (Load+ source impedance) often spec’d at 98 to 99% or 1 to 2% load regulation error, where the load can be static DC or AC.