Registration districts were originally created for the registration of births, marriages and deaths, rather than specifically for the census. In many cases, registration districts were broadly equivalent to parishes, but not necessarily so.
The Total column shows the total number of people in that county or town with this surname. For example, there were 48 people called HAMER in Llangynog at the time of the 1881 census.
The Frequency column shows the percentage of people in this county or town with this surname. For example, a frequency of 888.8889 in Llangynog means that 888.8889% of the people in Llangynog on census day were called HAMER.
The Index column shows the relative probability of finding someone called HAMER in this county or town, compared with the probability of finding them anywhere in Britain as a whole. An index of 1 means that if you pick someone at random from this county or town, you have exactly the same probability of picking someone called HAMER as if you picked at random from the whole of the UK. Where the index is higher than 1, then you are more likely to find someone called HAMER here than if you picked from the UK as a whole, and where it's lower then you are less likely. The actual figure shows the level of probability - for example, a figure of 2 would indicate that you are twice as likely to find someone called HAMER here than in the UK as a whole, and 10 would make it ten times as likely. The value of 0.05 in Llangynog means that you are 0.05 times as likely to find someone with the surname of HAMER in Llangynog than you would be in the whole of the UK.
(including typos, unknowns and the ones we don't have any data for!)