The external environment defines the opportunities and risks affecting a business. No business exists in a vacuum.
To take a somewhat intuitively obvious example, two elements of the external environment are seasons and weather. A clothing retailer should stock many warm coats, gloves, hats, and parkas in Minnesota but should focus more space on swimsuits and shorts in Florida. Retailers must respond to seasons (selling snowblowers in winter and air conditioners in summer), holidays, and local preferences as well (i.e. selling more conservative clothing in small Midwestern towns than in San Francisco or New York, which demand more extreme fashions).
Next, economic trends are part of the external environment. During economic downturns, people buy less expensive products, tend to repair older items instead of buying new ones, remodel instead of buying more expensive houses, and generally try to save money. Thus in such periods, retail and service firms should focus on opportunities in repair, selling generic inexpensive goods and other items that help people save money, such as cars that get better gas mileage or energy-efficiency upgrades for homes.
Interest rates are an important external factor in business decisions. If interest rates are low, it makes sense to borrow money and invest in expanding or innovating, but if interest rates are high, you may get a better return simply by sitting on a pile of cash that returns interest.
Another important element of the external environment is politics. For example, if one is thinking about where to locate a European branch, Brexit may make London less appealing than Paris, while political instability can affect many of one's decisions about investing in South America, Africa, or the Middle East. Similarly, for outsourcing manufacturing, one must assess political risks and economic issues such as exchange rates and wage trends.