Sequined dresses need to be washed with care. Turn the dress inside out and wash on a gentle cycle with cool water. Never put sequins in the dryer. Not only will they fall off, there is a good chance they could melt as well.
Formal dresses with beading on them should be handled similarly to sequined dresses. Turn the dress inside out, this will protect the beads from the washing machine. Put in the gentle cycle with cold water. Or, if you prefer to hand wash do it in cold water. Never put beads in the dryer they may fall off or melt on the dress
Dry cleaning is a special process of washing clothes that typically is not done at home. It is a good way to protect delicate fabrics. Water and detergents are harmful for some fabrics. Dry cleaning uses a special solvent that does not require water.
If your formal dress says that it needs to be drying cleaned, then it is important to heed that warning. This means that you could permanently damage the garment by washing it in water at home. It is not like they are saying your dress needs to be washed by a professional; it just means that the dress should not be exposed to water or detergent.