Non alcoholic beer that contains .5% or less alcohol and is aimed at those 18 and up or those wanting to watch their calories and/or alcoholic intake. Usually has the alchohol boiled out and is usually less flavorful and calorie rich than their alcoholic equivalents. Essentially Beer that you can't get intoxicated from. Usually labeled NA (Non Alcoholic)
O'Doul's and Sharps could be considered a "near beer".
Person 1: Hey pass me a beer
Person 2: Here is an O'Doul's.
Person 1: Don't give me that near beer crap. Got a real beer?