Every mutual fund has an annual dividend date on which it distributes internal gains and the tax liability on them. If you buy a fund just before the dividend date, which typically is close to the end of the year, you will pay a price that already has been factored into the dividend but you will owe tax on it. If you wait until after the distribution, you will pay the same price and avoid the tax. The same principle is true for selling fund shares. Sell them just before the dividend distribution.
The parents reduced their taxable income by $2,000 by timing purchases and sales around the dividend date. Since the parents income was taxed at the 20% tax bracket, the income reduction may decrease their income taxes by $400 ($2,000 x 20%).
If you are in a combined (federal, self-employment, and state) tax bracket of 20%, you could reduce your taxes up to $200 for every $1,000 of income reduction by timing purchases and sales around the dividend date.