I mean that you should tell a story, literally. Make the story about a single person, either a customer or consumer of your business or a decision maker in a company that’s part of the target market. Talk about who this person is. Give the customer a gender, an age, a family situation, and a problem to solve or a need or a want. Make it rich in detail. For example:

John Jones doesn’t particularly care about clothes but he knows he has to look good. He sees clients every day in the office, and he lives in a ritzy suburb, where he often sees clients by accident on weekends. But he hates to shop for clothes. (The Trunk Club)
Jane Smith wants to do her own business plan. She knows her business and what she wants to do, but wants help organizing the plan and getting the right pieces together. The plan needs to look professional because she’s promised to show it to her bank as part of the merchant account process. (Business Plan Pro)
Paul and Milena live in a beautiful apartment in Manhattan, with their two kids. Paul has a great job in Soho, Milena works from home, and neither has time for food shopping. (Just Fresh)
Acme Consulting has five people managing several shared e-mail addresses: info@acme.com, sales@acme.com, and admin@acme.com. The five of them have trouble not stepping on each other. Sometimes a single e-mail gets answered three or four times, with different answers. Sometimes an e-mail goes unanswered for days, because everybody thinks somebody else answered it. (EmailCenter Pro)
Notice that in each of these examples I could be much more general. The Trunk Club targets mainly men who don’t like to shop but need to dress well, and have enough money to pay for the service. Business Plan Pro is for the do-it-yourselfer who wants good business planning. EmailCenter Pro is for companies managing shared e-mail addresses like sales@ or info@. But instead of generally describing a market, I’ve made it personal.
Sometimes you can get away with generalizing. “Farmers in the Willamette Valley,” for example, or “parents of gifted children.” It’s an easy way to slide into describing a market. However, I suspect that you’re almost always better off starting with a more readily imaginable single person and let that person stand for your target market.