It sounds like you are talking about a ferrite bead (or ferrite choke or even just a ‘choke’)
When signal passes through the cord it can generate electromagnetic interface. Depending on the strength of the signal, what it is coming from and what it is going to this can be a small amount or a large amount. The cylinder is a magnetic material that helps dissipate the interference.
Depending on the application this interference can block or reduce the sign you are trying to send leading to a poor quality connection. In addition because the cable or device(s) can act like an antenna it can increase this interference which can be broadcast out. In the US the FCC has a lot of rules regarding things that produce electromagnetic or radio wave interference so in some cases these beads are legally required.
Some devices or cords will have the bead positioned inside the housing of the plugs themselves negating the need for it to be on the outside of the cord.
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