Did a friend, of a friend, tell you their uncle could do your lawn service for next to nothing? Somehow, I think that if you looked too close at that you'd find out he might have crashed his lawnmower into the last customers prized flower bed. If these things don't concern you then, by all means, don't worry about references. However, if you'd like to keep your envied iris in one piece, so that you've got a fighting chance in the next neighborhood garden contest, then it might just be in your best interest to look into just who is doing your yard service.
Protect yourself. Knowing that a company is willing to give you references is a comfort, and one that should be followed through. An honest lawn service company is going to give you valid and shining references, because, well, their happy customers are the ones that help their business grow. They'll be relying on those same references to not only tell you how well they've done but to spread the word to their neighbors, family, and friends. You'll know that they stand behind their work, and they aren't going to be taking the job for granted, because word of mouth will spread.
On the other hand a dishonest lawn care company naturally would be reluctant to give you any references, they aren't going to want you talking to the people whose property they may have damaged. Getting references will help you protect your property, and make sure you're finding someone who is going to do quality work, not forget to mow the back half of the yard.
Now, protect your pocket book. References also allow you an opportunity to ensure that the lawn care company you're hiring is sticking to their word. A dishonest company may say a yard care service is going to cost one thing, then start tacking on extras. With references you can ask questions about staying within the estimated price range, and if there were any unexpected costs. An honest company is going to give you the absolute best estimate they can, and then they are going to stick to that as closely as possible, and they won't dream of trying to throw in unexpected price changes, or undisclosed fees, lawn maintenance services, especially local ones, are looking for loyal and repeat business.
You're hiring someone to provide you with a service, and just like any other, lawn service is important, they'll be working on your yard, which can often be the first thing people see when coming to your home. A reputable lawn care company will be more than willing to share their references, and understand that you want to know what kind of work they do. It won't matter to them what type of project you plan to hire them for, be it a onetime yard service, weekly yard care or full landscaping, they won't hesitate to give you the contact information for customers who will attest to their work ethic, and quality.