The Geography of Ireland
"Ireland is sub-divided in a unique way; provinces into counties, counties into baronies, baronies into parishes, and parishes into townlands. The townland is a unique feature of the Irish landscape and is one of the most ancient divisions in the country." from the web site of George McIntyre.
Think of Ireland as a state in the US. Indiana is of similar land size for example. Think of Irish counties like counties in a state.
Think of townlands being similar to townships which fill up the counties of some mid-western states like Indiana and Ohio, BUT... there are many more townlands in an Irish county than townships in a US state. And... they aren't based on the a familiar Section/Township/Range layout like US townships are. They all touch adjoining townslands like townships do however, and fill up the Irish county completely. There is no place within an Irish county that isn't in a town, city or townland. Townlands can be as small as less than an acre, as large as 7,500 acres. They average around 325 acres in size.
Knowing what townland in which Irish county your ancestor lived in can be a major step forward in finding records for them. There are other divisions whose names you might find such as Dioceses, Probate Districts, (Civil) Parishes, Baronies, Poor Law Unions and Roman Catholic Parishes. A townland is generally considered to be the smallest area which defines where someone is located.
When you use the townland finding aids listed on the Web Sites page, you'll be able to find out where the townland exists with relation to these other divisions. Having Brian Mitchell's Atlas(1) at your side can be very useful in helping to locate a division (not a townland) where your ancestors lived and worked.
Check Donna Moughty's blog for more on the various administrative divisions:
Another good overview of the various divisions is the handout from Dan Poffenberger's Understanding Places in Ireland class at the Family History Library.
For sources of maps see the FamilySearch Wiki for Ireland Maps.
Also potentially useful for identifying a place name: The Origin and History of Irish Names of Places by P. W. Joyce (digital, V1, V2 and V3)
(1) Mitchell, Brian. A New Genealogical Atlas of Ireland. (See the Books page.)