Please see the Newspaper Article announcing the introduction of the Tracking Devices for an in-character explanation of the devices.
The Registry was created by the Ministry almost immediately after the war, in an attempt to keep tabs on those members of the population who seemed most dangerous, for whom they lacked enough evidence to incarcerate.
In the beginning, these individuals had a parole-officer of sorts, usually an Auror or other Ministry Official, who came on a bi-weekly basis to perform wand-checks to ensure no illegal spells had been used. These individuals were also under strict curfew to be indoors - and only inside their officially authorised place of residence - from dusk to dawn.
Registered individuals were known Death Eaters and werewolves, and also included immediate family members or shared-household members of those on the Registry.
As this almost included everyone, it rapidly became severely unpopular with the public at-large. The Ministry developed a Tracking Device to answer the cries of the populace for more freedom, while still maintaining control and monitoring of those dangerous members of the populace.
There are a few individuals who must wear the tracking device, as explained more fully below. For others, the device is optional, or they can continue to follow the Registry restrictions with wand-checks and strict curfew, though the curfew was also liberalised somewhat to be 10:00 p.m. to 6:00 a.m. on weeknights and 12:00 midnight to 6:00 a.m. on Friday and Saturday nights.
1. Collars -
These are made of leather, for maximum flexibility since they have to be charmed to alter shape with shape-shifters. The leather is completely impervious - won't get wet and shrink or stretch, etc. It is a wide-ish band about 1 centimetre in width. Remember that for many people, the tracking device is optional, as is the location of where to wear it. These are colour-coded as follows:
Black - Known Death Eater, either pardoned or having completed sentence for 'crimes'
Brown - Werewolf
Grey - Suspected Death Eater
White - Immediate family of known or suspected Death Eaters
2. Bracelets or Anklets - these are narrower, and can be made of metal rather than leather, though the Ministry is not paying for expensive metals. Probably nothing higher-quality than stainless steel highly burnished to appear 'silver'.
Whether the individual wears a bracelet, anklet or collar, there are magical rune etchings the devices which are visible to anyone who looks at them, to reveal its presence. For example, if Narcissa wears a bracelet, she might disguise it to appear to be all diamonds, but anyone seeing it would know that it was actually a Ministry device.
In the case of Bellatrix and Snape and anyone else where applicable, there is an additional 'marking' on their device which denotes them as having committed violent crime. Again this is a sort of magical glamour which is visible and recognisable by anyone, regardless of alterations made to the device. The exception to this is if the device is concealed beneath clothing and can't be seen at all.
Rules, restrictions, and capabilities of the device:
1. It is not possible to remove the device by normal methods. There is a (reluctant) safety measure - they *will* break/come off if enough pressure is applied to the device that the wearer is at risk of strangulation or amputation - but this will set off an immediate emergency signal at the Ministry and Aurors would appear post-haste. A new device would be provided, and if the individual is not found to be in a justifiable breakage or removal situation, Azkaban time would also probably be involved. Additionally, if the device is damaged beyond repair, a new one costs 500 galleons at the expense of the wearer.
The first device is 'free'. Very generous of the Ministry, don't you think?
2. Wearers are welcome to decorate their device as they choose, though they may not remove it to do so. This is a concession the Ministry had to make at the last minute - they had originally intended not to allow it to be tampered with at all, but a certain article had such popularity that they had to regroup quickly!
Altering the appearance of the device is acceptable, altering it's function is not. Any attempt to tamper with the functioning of the device will result in a fine or time in Azkaban, or possibly both.
3. The device informs the Ministry of the location of the wearer at all times. This is relatively specific, but not exact. Think global positioning device - it can tell that Snape is at 23 Spinner's End, or at Hogwarts, but not what precise room he is in, within the house.
It can detect if two 'tagged' individuals are in close proximity to one another, but it does not detect or know the identity of un-tagged people who are encountered.
It also has no capacity to record/'hear' conversations or non-magical activity or behaviour.
The device records every spell cast, every potion used, and every direct magical effect experienced by the wearer. For example, Snape could not ask Minerva to perform an illegal spell on him - like a transfiguration spell that might enable him to get out of the collar - in the hopes of getting 'around' the detection by not casting the spell, himself, because the device would record/detect the spell, anyway. However, it does not register every ward walked through in the sense of multiple wards on buildings, businesses, etc.
Who Gets What:
1. The following characters are Level I at this time, and must wear a device:
Lucius (may choose location of device)
Bellatrix (may choose location of device)
Snape (may choose location of device)
All Werewolves (must wear collars)
At present, Level I individuals must wait sixty-days after acquiring their device before being allowed to initiate the appeals process to decrease their status or potentially be removed from the Registry.
2. Almost everyone else on the Registry is Level II
You get to choose to wear a device, with all the 'freedom' that entails, or continue to report to the Ministry as before, with loosened curfew standards. You may also begin the 'appeals process' at once, to attempt to get off the Registry altogether.
3. Level III
Those folks who are on the Registry due to the original 'protest' staged by Harry and Ron at the beginning of the game - I *think* this is only Seamus and the NPC's at Fred and George's shop, but I'm not sure! You will be placed on Level III, and after a very perfunctory 'review of criminal history', you will be either removed from the Registry altogether, or advanced to Level II, whichever you, as the Mun, wish. ;)
Please reply here with any questions! We'll try to keep ironing out the details as questions arise.