Q factor of rlc series circuit
What is significance of Q factor in series RLC circuit?

Consider R, L and C in series to form a low pass filter like this: -

It will have a Q-factor of: -
$$Q = \dfrac{1}{R}\cdot\sqrt{\dfrac{L}{C}}$$
And, it will have a natural resonant frequency of: -
$$f_n = \dfrac{1}{2\pi\sqrt{LC}}$$
We might choose L and C values to produce a 1 kHz low-pass filter like this: -

The output signal frequency response (in red) has a 3 dB point at 1 kHz. Below that it's as flat in the pass-band it can be without any peaking. This is called a Butterworth filter (maximally flat). All three component values affect Q but, if we manipulate R, we can change Q without altering the natural resonant frequency, \$f_n\$. So, if R was lowered in value, we would see clear peaking:-

Now there's an undesirable peak in the response due to R lowering from 88.9 ohms to 8.89 ohms (Q changing from 0.707 to 7.07). But, what if we made R bigger: -

Now we have a rather sloppy low-pass filter and it is quite undesirable in many respects. Q has fallen to 0.31. So, in summary, the R value can be used to change the Q value of the circuit and, in doing so, it produces three different shapes for the low-pass filter frequency response.
On-line interactive calculator here.

Thanks, but what we achieve by getting right Q, why it is so
important?

Can you see in the example above (a common series RLC low-pass circuit) why Q factor is important to get right? This type of circuit is very useful in analogue-to-digital processing for avoiding &quot;aliasing&quot; (an ADC problem). It keeps the bandwidth of the filter maximally flat in the area of the spectrum we wish to sample and, progressively reduces high-frequency content that might cause &quot;aliasing&quot;.

Why RLC series circuits with larger Q factor values are considered
better?

Well, in the example above I hopefully showed how getting the Q-factor to the optimum goldilocks value sustains a maximally flat filter response with no peaking. However, some circuits require a high Q-factor such as band-pass filters. You can see from the resonant peaking in the pictures above that you could make a pretty phenomenal band-pass filter if you allowed Q to be very high. So the question then boils down to &quot;why do we need band-pass filters?&quot; and the answer lies in many applications such as radio transmission and reception, energy harvesting, a lot of switch mode regulation circuits, inductive power transmission, signal detection, frequency demodulation and many types of oscillators.
We even use software code to emulate band-pass (and low-pass and high-pass) filters. Everything about the conventional RLC filter can be transported into code and used to filter digital signals. And we'll still refer to the Q-factor as what it is, even in the digital domain.