It means in your direct maternal line, many generations ago you had an ancestor whose DNA matches those from the Iberian peninsula. Understand you got your Mitochondrial from only one person in each generation you go back. It is in no way your mother's total ancestry. Example: Get back to her 32 great great great grandparents and only one of them had her Mitochondrial.

In the overall view of world geography Lebanon is not all that far from the Iberian Peninsula.

Y & Mitochondrial testing are respected as being very reliable but a male gets each from only one person in each generation he goes back and a female gets Mitochondrial from only one person she goes back. Your ancestry doubles each generation you go back, 2 parents, 4 grandparents, 8 great grandparents, 16 great great grandparents, 32 great great great grandparents, 64 great great great great granparents and get back to about the 1200s the number of greats is in the 20s(don't remember the exact number) and if each were a different person they would outnumber the population of the world at that time.

Gilliam Name Meaning
English: variant of William, from a central French form in which W is replaced by G.

Source: Dictionary of American Family Names ©2013, Oxford University Press

BUT - BUT - BUT -

1) You have 16 great great grandparents. Only one of them started out life as a Gilliam. The other 15 could have come from other places. (And, if you are an American, probably did.)

2) If your Gilliam ancestor came from, for instance, France or Czechoslovakia, and his name sounded like "Gilliam" but was hard for people to pronounce, he may have changed it. I was helping a lady who thought she was a Pack, which is English, a couple of years ago. When we got to 1910, her ancestor was Pacek, a Czech who changed his name to Pack to seem more American.

Those are some of the reasons genealogists always tell people that surname origins are clues, not facts.

Please don't forget to choose a best answer. It doesn't have to be mine. 10 points aren't much, but they tell us you read the answers and we didn't flush 8 minutes of research and/or typing down the toilet.

With that exact spelling,
https://familysearch.org/search/
(the largest free genealogy site in the USA) has 918 records for it. By comparison they have over 150,000 for "Pack", which I know from personal experience is uncommon, and over 28,000,000 for "Smith". Here are the collections in the BMD category with more than 10 records, ranked by number of records:

Find A Grave Index 42 results
United States Social Security Death Index 35 results
United States, GenealogyBank Obituaries, 1980-2014 34 results
Texas, Birth Index, 1903-1997 33 results
Slovakia, Church and Synagogue Books, 1592-1910 23 results
California Birth Index, 1905-1995 19 results
Finland Baptisms, 1657-1890 18 results
Massachusetts Births, 1841-1915 18 results
Texas, Deaths, 1890-1976 16 results
Hungary, Catholic Church Records, 1636-1895 14 results

So, your choice, Finland, Hungary or Slovakia. You'd have to look up your ancestor to see where he came from.

With that exact spelling,
https://familysearch.org/search/
(the largest free genealogy site in the USA) has 596 records for it. By comparison they have over 150,000 for "Pack", which I know from personal experience is uncommon, and over 28,000,000 for "Smith". So, it is incredibly rare. It seems to come from Mexico. here are the collections in the Birth, Marriage, & Death Category:

Mexico Baptisms, 1560-1950 362 results
Mexico Marriages, 1570-1950 53 results
Texas, Birth Index, 1903-1997 27 results
Mexico, Distrito Federal, Civil Registration, 1832-2005 23 results
Mexico, Guanajuato, Catholic Church Records, 1519-1984 21 results
Texas, Marriages, 1966-2010 8 results
Mexico, Distrito Federal, Catholic Church Records, 1514-1970 3 results
Mexico, Chihuahua, Civil Registration, 1861-1997 2 results
Mexico, Hidalgo, Catholic Church Records, 1546-1971 2 results
BillionGraves Index 1 results
California Birth Index, 1905-1995 1 results
Kentucky, Vital Record Indexes, 1911-1999 1 results
United States Social Security Death Index 1 results

I have no idea what it means.

I am Sicilian but I live in the US. Growing up my grandpa told me that his dad (my great grandpa) was adopted by my great great grandparents. There is some crazy story that went with it and I'm not sure how true it is but I do know that he was adopted. My great grandpa and my great great grandparents immigrated to the US and I have never met them, (they passed before i was born) I'm not interested in finding long lost family but i am interested in knowing a little more about my heritage.

My grandpa died 3 years ago so I'm trying to use the internet. Does anyone know of a good website or how to do this type of research? Thanks!

Nope, not a hope I'd trust the results. Their tests are not looking for specific genetic issues and it isn't lab certified. At best you have something to entertain you. Worse case scenario you have misleading and outright wrong data. They clearly state it's to connect you with your ancestors. It is not meant as a medical evaluation.

In case you missed it, 23 and me is facing lawsuits for it's faulty data and was yanked for awhile by the FDA because it isn't a valid clinical analysis. They've also been smacked down by the FDA for their misleading advertising regarding DNA relevance. http://www.the-scientist.com/?articles.v...
http://www.businessinsider.com/23andme-c...