I hope this isn't too much of a shock for you, but your clients generally do not care about the law. At all. What clients want is to for you to solve a business problem so that they can get back to doing business-y business things with other business people. (This is literally what your first few client briefings will sound like to your untrained ear.) Don't be seduced by the occasional client who seems intrigued by the nuances that you have teased out in your research. Clients are intelligent, inquisitive and driven, and sometimes they may say things like "Oh! that's interesting!" and you will think that they care about what you do. Don't be fooled. As highly competent managers of people, they are able to be charming, affable and engaging, even with you. But their apparent fascination will end disappear abruptly when they remember that your firm is charging them by the nanosecond.
So, to serve your client well, you need to be able to treat legal problems as business problems. And to solve these business problems, you need to understand business in general, and your client's business in particular. Only then, can you start to see how completing the work you have been assigned helps that business to work better.
That can be difficult. There's only so much you can learn from company documents and internet research. The best source of what clients want and need, are the clients themselves. Unfortunately face time with clients is a jealously guarded commodity. This means that associates tend to observe business from within the safe, sheltered confines of a research memo, or hear the rumblings of commerce from deep within the bowels of a large transaction. But there are a couple of ways to counter this problem. The first is to to do a little self study of basic economics. A passing familiarity with supply and demand curves, market failures and externalities can be really helpful. The second, and more important one, is to spend time with people who buy and sell for a living, and learn to watch markets in action.
If you do that, you will start to recognise that a business is, at its core, a machine for supplying goods and services to the market, in response to market demand. Lawyers, consumers, and even owner and employees of businesses can sometimes forget this! This is because many (perhaps most) of the people who work in business organisations are one or more steps removed from the customer. It's can sometimes be because a business is so stable that it hasn't had to look for a new customer for a years, even generations! But it can also be down to the fact that business organisations are far more than just commercial constructs. In addition to being enterprises, they are social institutions, political organisations, even extensions of government. And all these roles can eclipse the core purpose for which they were formed.
But it is vital to remember that while businesses can be large or small, complex or simple, they are all essentially machines for meeting a market demand. The clearer the line you can draw between the work you have been asked to do, and the success of the business you have been hired to serve, the more efficient, effective, (and endearing) your clients will find you.