Why is Chandrasekar Limit expressed relative to Sun? In 1931, Chandrasekhar was able to show that there is a certain critical mass (Chandrasekhar's limit) beyond which a white dwarf cannot exist, since the electronic fluid at that point cannot support its weight no matter how compressed it is. 

The core of such a star will simply collapse inward. 

The critical mass, Chandrasekhar showed, is 1.4 times that of the Sun.

When I first heard this, I was totally confused. Sun is a star too. The Sun will eventually enter the Red Giant Phase, and then it will eventually become a white-dwarf.

How and why did Chandrasekar express his limit relative to Sun?
The mass of the sun is just a unit of convenience in a astronomy. The sun's mass and luminosity, in particular, are relatively easy for us to measure precisely, and when we're talking about stars, provide a convenient scale where the numbers won't be too "astronomical" (be too high a power of $10$ to picture easily). You could derive the Chandrasekhar limit in grams, kilograms, or slugs from the relevant physics, if you wanted. The relevant equation (from the Wikipedia article) is:
$$M_{\mathrm{limit}} = \frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu_e m_\mathrm{H})^2},$$
where $\mu_e$ is the average molecular weight per electron (stellar composition dependent), $m_\mathrm{H}$ is the mass of hydrogen, and $\omega_3^0$ is a numerical constant that is approximately $2.018236\ldots$.

It should be noted that the Chandrasekhar limit is a limit on the mass of the final white dwarf, not of the object that will produce the white dwarf.