The shield of a coax cable isn’t a wire with one surface – it is a cylinder with two surfaces, an inner and an outer. This means that, provided its thickness is more than a few skin depths at the frequency of interest, you can have a current flowing on the inside of the shield and an entirely different current flowing on the outside!
Every coax fed antenna system designed to have specific characteristics needs a current balun located at the transition between balanced and unbalanced. These are often built into VHF and UHF antennas (skirts, sleeves, etc.) but are generally separate items in HF systems.
Without a current balun the antenna is strongly coupled to the outside of the coax shield.
This means that energy transmitted by the antenna will be coupled into the coax shield which will reradiate it and thereby affect the radiation pattern of the antenna system.
It also means that signals picked up by the coax shield acting as an antenna will be coupled into the antenna and passed to the receiver.
It is important to note that, like any other conductor, the coax shield will pick up signals and re-radiate them. The current balun simply ensures that these re-radiated signals don’t get coupled into the antenna and so don’t reach the receiver.