What do you mean by quantum nature of charge ?

The quantum nature of charge means that charge cannot exist in any random amount. It is always found in fixed amounts.

The charge on a body is always an integral multiple of the charge of one electron.

q = ±ne

where (n = 1, 2, 3, 4, ……) and
e = charge on an electron = 1.6 × 10^-19 C.

So, a body can have charge like (+e), (-e), (+2e), (-3e) etc., but it cannot have charge like (1.5e) or (0.9e).

Thus, charge is said to be quantised.