H NMR of 4-chloroacetophenone
The further to the left a peak in an NMR spectrum is, the more deshielded it is. Deshielding or shielding are terms to describe how much a certain nucleus is shielded from the outer magnetic field that is applied during NMR measurements. Shielded nuclei will experience less of a magnetic field and thus resonate at a lower frequency meaning lower ppm-values; and vice-versa. In general, shielding can be explained by more electrons being in the vicinity of an atom because the electrons — in layman’s terms — can be thought to create an electric current induced by the outer magnetic field, which in turn generates an opposing magnetic field and lowers the effective magnetic field at a nucleus.

If we have an electronegative atom close by, that atom will draw electrons towards it, reducing the electron density around the nucleus we are observing and thus deshielding it. That not only works for electronegative atoms alone, but also for electron-withdrawing groups like the carbonyl group.

In your specific example we have two electron-withdrawing groups that will deshield neighbouring protons. However, the deshielding that the acetyl group is responsible for is stronger than that of the chlorine atom. So both pairs of protons are moved downfield (to higher ppm values) when compared to toluene or para-xylol, but the protons closer to the acetyl group are deshielded more.

It ultimately boils down to oxygen’s electronegativity in combination with an $\ce{sp^2}$ carbon that is not attached to any hydrogen, but it may be easier to think of carbonyl groups being electron-withdrawing per se.