Because MAs lag. So you shift them forward to account for the lag. See Joe DiNapoli's publications. He likes simple MAs shifted to the right.
I had an a-ha moment with shifted MAs when I was graphing my gas mileage recently. I entered the mileage for every fill-up for the last 9 years for my car into Excel - the fill-ups were close to weekly. Then I put a 10 period MA on it and graphed the result. I noticed right away that the MA was almost sinusoidal and realized it was seasonal variability. i.e. better mileage in the summer, worse in the winter. I further noticed that the lows in the MA were in April which didn't make sense since I'd expect the low to be in the Jan-Feb time frame. Well, if you shift the MA back by 10 periods, the lows were in the Jan-Feb time period. The conclusion: MAs are lagging, and you can compensate for the lag by shifting if and only if there is a periodicity to the data. If the data doesn't have some inherent periodicity, then shifting wouldn't tell you much. What's this mean to price charts? Well, if you suspect that your instrument's price action has periodicity then shifting the MA might be enlightening. Seasonality for retailers comes to mind due to Xmas. Price trends synched to quarterly earnings reports is another obvious one.
Shifting is just curve fitting the MA to the price. Like all indicators, it is still backward looking and has no direct predictive quality. The way I personally use MAs is to pick a time period and just do a simple analysis to see if price is above or below the line. I have started using price patterns to generate potential buys or sells, and just filter the results with the MA analysis. In other words, buy if the pattern is bullish, and price is above a given MA, or sell if the pattern is bearish and below a given MA. And of course use money management and risk based exits.