Your net worth is a single number that describes how (monetarily) wealthy you are at one point in time. It is calculated by subtracting the sum of your liabilities (debt) from the sum of your assets (also known as a balance sheet). In other words, your net worth is what you own minus what you owe. As a graduate student, your net worth might be negative, close to zero, or positive.
Your net worth is only a snapshot in time, so it is useful to track how your net worth changes with time – both the direction and rate of change. If you are taking out student loans to fund your graduate education and/or living expenses, your net worth is likely decreasing. If your stipend barely covers your living expenses, your net worth is likely fairly static. If you are currently saving money, paying off debt, and/or your investments are increasing in value, your net worth is likely increasing.
To build your wealth over time and to eventually become financially independent or retire, your objective is to increase your net worth by increasing your assets, decreasing your liabilities, or both. Due to the power of compound interest, as your total invested assets increase, your net worth on average also tends to grow even faster.
Further reading: What is Net Worth?, What Does Your Net Worth Really Mean?
While it is useful to know your net worth, do not allow its absolute value or even its direction and rate of change to impact your emotional self-worth. Your net worth is not a reflection of your value as a person. While achieving (or being given) a positive and/or increasing net worth during graduate school gives you a nice start in life, it alone does not determine your continued financial success. Likewise, having a negative or decreasing net worth in graduate school does not doom you. As a graduate student, you are just starting your career, which ideally will be long and financially prosperous. If you are taking out student loans during graduate school, the liability side of your balance sheet is growing, but the asset side does not take into account the knowledge, skills, experience, and network that you are currently gaining that will help you greatly increase your income and net worth in the future.