So what is Patronymics?
Concentrating on Wales, the easiest way to describe it is the son takes the fathers Christian name (first name) and that becomes his surname. For example, if the son is called WILLIAM and the fathers full name (Christian and surname) is REES THOMAS, then the son William will be called WILLIAM REES (or maybe William Reece). If in turn this WILLIAM REES has a son JOHN he will be called JOHN WILLIAMS. (Note: Often an "S" was added to the surname, so William would be Williams, and names like David or Rees when changed into a surname became Reeces or Davis).
Thus, each generation you go back the surname changes.
It is important when doing research in Wales to remember the existence of Patronymics, and travel along the research road with a bit more caution. It may be that your family dropped Patronymics a long way back so it may not affect you, but it's wise to bear it in mind.
This naming custom first appeared way back in the 12th century, but how long it continued varied from place to place. In some areas it carried on until the 19th century. It appears the more wealthy families tended to leave the patronymics behind a lot earlier than some communities in rural outcrops, that weren't influenced by the modern tide of using a fixed surname.
A mentioned earlier, this is not just a Welsh anomaly. The Norwegians only passed a law back in 1925 to change the naming custom to the fixed surname, the one we all use today. Pre-1850 most Scandinavian countries used patronymics. The Russian patronymics custom was to name the child by a Christian name, and then its middle name would be the father's Christian name, plus and ending. So it is not just Wales standing alone here .
The problem, though, with research is that patronymics didn't stop all over Wales at the same time. It began to die out in some areas much earlier than others. Plus, the other handicap is that there aren't a vast amount of different surnames in Wales; hence, you will find a prominence in names such as Williams, Jones, Thomas, Jenkins, Reece, Preece, Evans, Lewis, Davis, etc. You will find in Welsh communities a mass of people with the same surname and not the slightest bit related to each other.
Also, women kept their maiden names when they got married, and prior to marriage the word "ferch" was used, meaning "daughter of." For example, MEGAN FERCH THOMAS, was MEGAN daughter of THOMAS.
Another way of naming the son was the use of "ab" or "ap", a shortened version of "Mab" meaning "son of "in Welsh.
Hence, you could have DAFYDD (David) AP THOMAS AP REES AP OWEN, meaning, DAVID, son of THOMAS, son of REES, son of OWEN.
A general rule of thumb is that for most families, fixed surnames were adopted by 1812. Indeed, this is the cut-off period accepted by the Church of Latter Day Saints with the International Genealogical Index (IGI).
Leaving patronymics aside, there are a couple of other points to bear in mind when researching in Wales. Actual Church (and court) records would be in Latin and English, but you may encounter the Welsh language in other areas such as place names and peoples names. Road signs in Wales today are in both Welsh and English. It is very apparent that the Welsh name for a place has not the slightest resemblance to the name in English. Hence, a good starting point for Welsh research would be to join one of the Family History Societies in the region of Wales you are searching.
Additional IInformation:
WELSH WILLS PRE-1858 are searchable online at : www.pro.gov.uk
THE NATIONAL LIBRARY OF WALES,
ABERYSTWYTH, DYFED, SY233BU, WALES