Well that is exactly what it is. Now, many vacuum cleaners past & present (though less so today) have required an earth wire. The reason for this is that there are metal parts on the cleaner which are considered potentially liable to come into contact with a live wire, in rare circumstances. How this is decided and who decides it I don't know as this is not my area of expertise. A lot of Wet & Dry cleaners had earth wires, as did a good many older dry vacuum cleaners.
Most cleaners are double insulated, which in it's basic form means that there is enough none-conductive material between live parts, even if a live wire became loose. A rating plate will usually indicate whetehr or not an appliance needs an earth, by saying the words earthed / double-insulated, or by displaying the respective logo. You will have to search Google for that.
However, a lot of DIY people replace flexes on appliances, and get it wrong. The two worst things which someone could do would be to fit a flex which was too thin for the job it was required to do, and fitting a 2-core flex to an earthed appliance. Other issues are using ordinary PVC flex on items like irons, not fitting cord clamps correctly, and so on. On vacuum cleaners, a classic trick is to use three-core flex to replace a two-core. Although there is essentially nothing wrong in that, the earth wire needs to be cut right back at both ends for it to be safe. It is just rather sloppy practice to use three-core, if nothing else. But it is sometimes very impractical too, as getting it through the cord sleeving and grips can be difficult if the flex is thicker. Also as I said earlier, the three cores make twisting much easier and on a vacuum cleaners the cores will eventually overlap and twist as a result of winding & unwinding the lead.
The worst possible use of three-core flex comes from a DIYer deciding to fit a three-core flex and utilise the earth wire by attaching it to a metal part of the appliance. There is no need for this if the cleaner is clearly marked as being double insulated and in some cases it can be argued that it makes the appliance more dangerous, should the earth wire ever get disconnected and made contact with the live. However, that could probably be said of any earth appliance.
