Personal finance is the financial management which an individual or a family unit is required to do to obtain, budget, save, and spend monetary resources over time, taking into account various financial risks and future life events.
When planning personal finances, the individual would consider the suitability to his or her needs of a range of banking products (checking, savings accounts, credit cards and consumer loans) or investment (stock market, bonds, mutual funds) and insurance (life insurance, health insurance, disability insurance) products or participation and monitoring of individual- or employer-sponsored retirement plans, social security benefits, and income tax management.
The goal of personal finance is not necessarily to get rich, but more importantly to obtain and guarantee freedom (financial, social, etc). The rule of thumb is to spend less (incrementally less) than you get.
vCalc's Personal Finance folder contains equations to help an individual compute personal finances.