The books refered to are the index record books of all births deaths and marriages. After 1837 all births deaths and marriages had to be registered. These were recorded in books at the registry offices. The books are no longer available to look at as they were getting too damaged by researchers. In place of the books are index records that identify individuals and give a reference to book and page on which the original details are held. If you ask for a certificate from the Public Record Office they will reproduce a copy of the original entry to create a birth, death or marriage certificate. This of course is user pays, at around 6 - 8 pounds a time. The PRO web site provides lots of info on family history research so you probably want to visit it ( http://www.pro.gov.uk/http://www.pro.gov.uk/ )
Index records are held on microfiche (plastic films) that are often held by county libraries or local genological societies. Failing that contact your local Family history centre under the Church of Latterday Saints in the phone book.
The kensington record I provided is for May Ann's birth and the Fulham record is of her marriage. If the marriage had been after 1912 then the surname of her partner would have been on the index record. Since its not you need to get a copy of her certificate to see who she married, her address and who the witnesses were. If you obtain the birth certificate it will give the names of the parents and the address they were living at.
The index records show 2 different spellings of the name which is not unusual as lots of transcription mistakes were made when creating the indexes.
I cannot be 100% sure that the index records are of the person you are looking for but I would say its 90% based on my quick check.
I have copied all maslin index records from 1837 - 1940 so far and I'm working on the rest. If you look elsewhere in this forum you will see followups from David Maslin. David has copies all Maslin and Maslen index records and lots of others from church records. With luck you should be able to trace from 1550 - present day with a bit of luck and perseverance.
You also need to look on the web site for the Church of Latterday Saints who have spent years collecting family history records and this is where you will be able to trace back pre 1800.