Hello Sinwoo Cho,
from the documentation on Slot:
# represents the first argument supplied to a pure function.
So, e.g. Sin[#]& is the same as just Sin.
When you want to plot the result, you need to choose numerical values for all parameters,e.g.:
func = DSolveValue[y'[x] == +a*y[x]^3*(y[x] - p), y[x], x];
ReImPlot[Evaluate[func /. {C[1] -> 0, a -> -1, p -> 2/3}], {x, 1, 4},
PlotRange -> All, ReImStyle -> {Red, Directive[Thick, Dashed]}, ReImLabels -> "Text"]
