a quick run down of Irish land divisions, and how they apply to where your Manley family lived in 1901 ..
the main division, going largest to smallest :
County - 32 of these on the Island of Ireland. The county town of County Wicklow is also named Wicklow. Other major towns include Arklow, Baltinglass, Bray, Carnew and Rathdrum (there are no cities in Co. Wicklow).
Barony - about 370 of these, 10 of which cover parts of Co. Wicklow. The townland of Ballynabarny, where your Manley family are living in 1901 is located in the Barony of Newcastle. Barony names are not used that often in Family History research, but are sometimes included to differentiate different townlands or civil parishes which have the same or similar names. e.g. There are two townlands in Co. Wicklow named Balinabarny - one in the barony of Ballinacor North, the other in Upper Talbotstown.
Civil Parish - there are over 2,000 of these, and just under 60 cover parts of Co. Wicklow. Ballynabarny townland is in Glenealy civil parish. Civil parishes were usually the same as the local Church of Ireland parish.
Townland - over 64,000 of these, about 1,400 of which are in Co. Wicklow. Townlands are the smallest division of land and these range in size from less than an acre, to several thousand acres.
Other important divisions :
Registration District - this is the area that civil Births, Marriages and Deaths were registered in, and these were usually based in the larger towns. The registration district for the area around Ballynabarny was Rathdrum. These districts derived from Poor Law Unions, and generally covered the same area, and had the same name.
Catholic Parish - the area covered by an RC parish. These sometimes corresponded in name and area to civil and Church of Ireland parishes, but often had different names. They could cover a single civil parish or a number of these. Parish boundaries could alter over time as populations changed. A parish would have a single parish church where records were kept, and could have a number of chapels of ease around the parish for easy access. Two possibilities for the RC parish for Ballynabarny, Wicklow and Ashford - with the parish churches being in the towns of the same name.
Town - these are population centres and are often based in a townland of the same name. Nearest town to Ballynabarney is Glenealy.
Village - smaller population centre than a town.
for reference here's a link to an early OSI map showing the townland :
Ballynabarney townland (c1837)
(the townland borders are indicated in red)