I must confess, this is one homebrewing practice I have never come across. What you are describing is, however, practiced by almost every large commercial brewery in the world and is called high-gravity brewing (HGB).
The whole idea behind HGB is that a brewery can expand its production capacity by simply starting with a higher-gravity wort and adding water to the finished beer right before packaging to adjust the beer to its “normal” strength. Suppose Wizard Pale has an original gravity of 1.052 and I brew 1 million barrels each year. If I simply increase my original gravity to 1.056 and add water prior to packaging, I can expand my production capacity by 80,000 barrels per year with very little capital outlay.
There is more to this method than meets the eye. For starters, adding water after fermentation is tricky because you have to do some calculations to know how much to add. Too much and the beer is weaker than the target; too little and you have a stronger beer. In commercial breweries these calculations are made by using both the alcohol content and the specific gravity of the beer to back-calculate the wort original gravity. At home if you are supposed to have five gallons of 1.048 wort but instead start with four gallons of 1.060 wort, you can add the missing gallon of water at the end.
The other thing about adding water to beer is that water contains oxygen. If you simply add tap or bottled water to fermented beer, you will immediately add plenty of oxygen to start beer oxidation. “Blend water” as it is called is brewing-quality water that has been de-aerated and carbonated. This is fairly easy to do at home if you have a keg. Simply boil the water and cool, keg, and carbonate it.
All of this work is meant to expand your fermentation capacity. If you want to brew five gallons and have a five-gallon fermenter, this whole process is a waste of time. Many homebrewers don’t have brew kettles large enough to boil their entire batch, so water is added after boiling to adjust the wort volume and wort gravity. That is a sound practice that truly makes sense at home.
I know some brewers are going to read this and get all sorts of clever ideas. So to complete the list of HGB pitfalls I must mention wort original gravity. You cannot make a normal-tasting “regular strength” beer by starting with a barleywine. I can hear the thought process now: “If I can make five gallons of 1.100 wort and ferment it, I could stretch it to 10 gallons of beer!” Unfortunately this doesn’t always work because very high gravity worts tend to produce beers with much more fruity esters than their normal-strength cousins. A diluted barleywine most likely will taste just plain funky.
Most big brewers don’t go much higher than about 1.065 because of this and are very careful about wort aeration because poor wort aeration results in the production of more fruity esters. There are some big brewers dabbling in VHGB (“V” for very). They start with worts as high as 1.100. Wouldn’t you hate to be a yeast cell in those breweries!
Like I said, I have never heard of homebrewers using this technique. My advice to a starting homebrewer is to ferment a full batch of wort and not add any water to your batch once fermentation begins. This will allow you to check your wort specific gravity before starting fermentation, and you are not left wondering if the beer should have tasted different because of adding too much or too little blend water.