Estimated taxes are payments you make yourself, outside of paycheck withholding, when withholding will not cover your full tax. The IRS expects tax to be paid as income is earned, so it sets four deadlines: April 15, June 15, September 15, and January 15 of the following year. Miss the mark and you owe an underpayment penalty, essentially interest, even if you pay the full balance in April.
Salaried people with only wages rarely need them. They become relevant when income arrives without withholding: freelance work, large capital gains, ESPP sales, or a big RSU vest withheld at 22% when your rate is 35%.
The safe harbor makes it manageable. If your combined withholding and estimated payments reach 100% of last year's total tax (110% if your adjusted gross income was over $150,000), there is no penalty regardless of what you owe this year. So someone whose tax was $40,000 last year with $150,000-plus of income needs $44,000 paid in by January 15, through any combination of withholding and estimates.
The common mistake is skipping estimates and planning to settle in April, then paying a penalty on top. A simpler route for employees is often to raise W-4 withholding instead, since withholding is treated as paid evenly through the year even if it all happens in December, while estimated payments are judged by their dates.