There are a lot of reasons to shop local when you can, one of which is your local economy. A purchase from a local business (big or small) creates a cash cycle within your economy as oppose to a cash chain where your dollars get passed down the line and right out of your community.
HOW IT STARTS
These big box stores that move into a city don't stimulate the economy more or attract a mass of people living outside of a city to visit, they simply shift where money is currently being spent. The population doesn't all of a sudden start spending more money because a Walmart moved into town. They stop spending their dollars at existing businesses and start shopping at the large chain due to convenience, lower cost or selection.
A study found that 85% of sales for a new Walmart came at the expense of existing businesses in that area and only 16% were new sales from people outside of the city, attracted to the big new store (source).
WHERE DOES THE MONEY GO?
When a company has several chains across the country, they have a head office somewhere (most likely not in your hometown unless you live in a big metropolitan city). In general, this head office houses a huge team that takes care of things like production, marketing, accounting, legal issues, human resources, business development, buying, supplies, etc. Wages are paid to them, instead of someone in your community. This is all good for the city the head office is located in as those employees will spend the majority of their wages there, stimulating their local economy but your town will most likely never see that money again.
HOW DO LOCAL BUSINESSES DIFFER?
Local, independent business are often more conscious about where they spend their dollars. They will hire local architects, designers, signage companies and contractors to build their store, local service providers to care of things like their accounting and legal issues. They'll advertise in local publications and pick up office supplies locally as opposed to having them shipped in by a head office. Those dollars follow the same cycle with the local businesses they were spent at. That local accounting firm will spend their money on local suppliers and service providers.
Local business owners usually have more of an interest in their community and will in turn contribute to local organizations, events and charities. They have ties to their city and aren't going to just pick up and move to another city in hard economic times.
Supporting local doesn't take a huge change to make a difference. Sometimes shopping a large chain fits into our lives based on time, cost, convenience and stock. But shifting just 10% of your monthly spending from large chains to local restaurants, shops and businesses can make a huge impact on your community.