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 30 people called TATE in Hesleyhurst 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 689.6552 in Hesleyhurst means that 689.6552% of the people in Hesleyhurst on census day were called TATE.
The Index column shows the relative probability of finding someone called TATE 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 TATE 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 TATE 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 TATE here than in the UK as a whole, and 10 would make it ten times as likely. The value of 0.03 in Hesleyhurst means that you are 0.03 times as likely to find someone with the surname of TATE in Hesleyhurst than you would be in the whole of the UK.
(including typos, unknowns and the ones we don't have any data for!)