In the past I've written about proactive customer service. The example I always like to use is when a server in a restaurant notices a guest's water glass is half full and refills it before the guest has to ask for more. Being proactive raises the perceived value of what you offer. Your customers feel you're really paying attention and focusing on them and their needs.
Recently, I've seen a phrase I believe takes things a step further and that's "anticipatory customer service." It's a step beyond proactive customer service (though there's a gray area between the two). Being proactive means responding to a need before a customer voices it (such as refilling a glass of water). Anticipatory customer service, however, is about being one step ahead. It's intuitive. It's not just noticing a need, it's anticipating it. For example, you call a customer and he says "I was just getting ready to call you." One step ahead.
When I was a teenager, I had a thriving magic show business which catered to birthday parties. My dad used to tell me I had to be at least 20 minutes early to each party. He explained that about 10 to 15 minutes before the party was to start, parents would begin to worry that I wouldn't show up. It didn't matter that I knew I would be on time. It was about them. So, anticipating that they might worry, I made sure I was always early.
Anticipating your customer's needs is like a game of chess. The best players don't think only of the next move. They anticipate the next four or five moves and try to imagine how their opponents will react to each move. You, too, should always try to be at least one or two moves ahead of your customers and anticipate what they might want or need.
This high level of service is about being in tune with your customers and getting them what they need before they ask for it (or even know they want it). It shows that you're customer-focused and strive to deliver an amazing customer experience.