Although many countries have an income tax, this node will focus on the United States.
An income tax refund means that you have paid the United States Government too much money, and they return the overage to you by means of a check or direct deposit.
An income tax refund isn't necessarily a good thing.
Because you've overpaid, you've given the government a free loan with no interest. If you calculate your taxes properly, you can take that amount and use it to pay down your interest-bearing charge cards, which will help you in the long run. Additionally, you can use it to build up a savings cushion in case of a financial catastrophe, such as losing your job.
For some folks that have severe difficulty saving a single cent, it can be thought of as a forced savings account that can only be tapped around tax time. For those folks, I recommend calculating their income tax accurately and getting the difference placed into savings bonds. The amount it generates in interest is not very good, but they are semi-liquid and are enough of a pain in the ass to prevent most folks from cashing them in to go buy Assassins Creed IX.