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I read somewhere that in some cases, it might be easier to study symmetric slabs. Can anybody help me tell in what cases it is easier?
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it is easier if net dipole moments can be avoided. In principle, additional symmetry operations reduce the size of the irreducible part of the Brillouin zone. However, for slabs, along the surface normal just 1 k-point has to be taken anyway.

A slab has two surfaces. By symmetric slab, I mean slab whose both sides are studied. So far I considered only one side of the slab, the other surface(bottom) is terminated by H or any passivating group to cap dangling bonds. My
question was: when we study symmetric slabs? The answer above is not very clear and could be in different context i.e. a slab which is symmetric.
Could you assist me know when both sides of the surface are studied?

To my knowledge, there's no real problem with using a "symmetric" slab. However, this means that your double-sided slab thickness will have to be greater than your single-sided slab in order to have a satisfactory amount of bulk-like layers (and potentially more vacuum, too). So the only real problem is that your system will most likely be considerably larger. Otherwise, from my experience and what I've seen in the literature, it's fine.