Conscious parallelism is when a business aligns its prices with that of its competitors without colluding with the competitors to keep prices at a certain level. This would be the opposite of price fixing, which is illegal for businesses to undertake in.
Markets find a price for products that consumers are comfortable paying, and then all businesses that sell that same product tend to align their prices so that they remain competitive.
Conscious parallelism is not illegal because there's no collusion happening between competitors. However, it is seen to be harmful because it keeps prices artificially high. It can be difficult for prosecutors to prove collusion, and a business will often use the defense of conscious parallelism if they are being charged with price fixing.