Why we measure bandwith at -3dB?
It is a common value because at $-3 \ \mathrm{dB}$ the power of the signal is reduced to half its value. I'll show a brief example to make it clearer.

Suppose that you have a signal whose amplitude is $1 \ \mathrm{V}$. If we reduce its amplitude by $-3 \ \mathrm{dB}$, the new amplitude would be close to $ 0.707 \ \mathrm{V} $.

The power of a signal is proportional to the square of its amplitude. For simplicity, let's assume a resistance of $1 \ \Omega$ on which we are going to calculate the dissipated power. Therefore, originally we would have had a power of $$(1 \ \mathrm{V})^2\cdot\frac{1}{1 \ \Omega}=1 \ \mathrm{W}$$

But after the reduction, we have a power of

$$(0.707 \ \mathrm{V})^2\cdot\frac{1}{1 \ \Omega}=0.5 \ \mathrm{W}$$

The power has decreased to half its original value. That is why the $-3 \ \mathrm{dB}$ point is commonly used to characterize frequency-related properties.