A precinct is the smallest geographic unit that is used to make up election ballot groupings and usually contains between 1-1,400 voters. The numbering schemes vary between counties, but precincts can be considered a small neighborhood area.
Here’s a breakdown of Virginia’s presidential election results in 2008 by precinct:
A ward is a unit that represents part of an electoral district or municipality, used in local government elections. Also, a ward can be comprised of several precincts.
Below is a map of Minneapolis that compares wards versus precincts