You buy a smallish house in a suburb and pay $1000/month for you mortgage. $900 of that goes directly to equity.
At the end of the year, if you home retains its value, you have over $10,000 in equity.
If you pay the same amount for rent, you have nothing to show for it. And oftentimes rent for an equivalent house is actually more than the mortgage + tax payments.
So, which is better $10,000 or $0?
The volatility of the last few years has complicated this a bit (people going underwater, for example), and I don't think people should see a home as a vehicle for getting rich, but it is generally a nice value store.
Plus, there are HUGE advantages for people invested in the area to own their property. It is more stable for them (they can't be kicked out), they are more likely to invest in the value of their area (volunteerism, making sure local politicians take care of the parks, reporting crime, that kind of thing).
Edit: Let me point out that yes, these numbers are made up and don't accurately reflect reality. I did not use a mortgage calculator or anything (I thought that would be obvious) but the underlying idea that I was trying to convey holds....if you are spending x dollars and are able to store any portion of that in something that holds some value it is better than spending x dollars and not storing any of that value. So, even if only $10 of every $1000 spent on the mortgage goes into equity, it is better than $0 if you rent.