Here's what the IRS says about underpayment penalties:
Penalty for Underpayment of Estimated Tax
If you didn’t pay enough tax throughout the year, either through withholding or by making estimated tax payments, you may have to pay a penalty for underpayment of estimated tax. Generally, most taxpayers will avoid this penalty if they owe less than $1,000 in tax after subtracting their withholdings and credits, or if they paid at least 90% of the tax for the current year, or 100% of the tax shown on the return for the prior year, whichever is smaller. There are special rules for farmers and fishermen. Please refer to Publication 505, Tax Withholding and Estimated Tax, for additional information.
If you have paid 100% of your previous year's total taxes in advance (through a combination of withholding and manual "estimated tax" payments), the tax forms for the next year won't tell you that you owe an underpayment penalty. There's a line on the tax forms for entering the total amount of estimated payments you made for that tax year, and the IRS presumably matches that up with their records of how much you actually paid them in advance through the online system to make sure you put in the right number.
If you don't make any extra estimated tax payments, and the withholdings your employer computed for you based on your W4 fall more than $1000 short of the actual tax you end up owing (which includes things like capital gains income, loan forgiveness, and other stuff you had no way of predicting and no mechanism or reason for informing your employer about in advance), then you can owe an underpayment penalty, apparently as punishment for not predicting the future.
(Also, some states have basically the same system, so when you pay extra money to the IRS to avoid underpayment, check to make sure you are also paying your state enough to avoid underpayment.)
In theory there's a quarterly breakdown of when you are supposed to pay the estimated tax if you are required to pay it (as computed by the 1040-ES form), but I haven't been able to find any information on the penalty for paying late, other than the final underpayment penalty on your return for the tax year. And if you aren't required to make estimated tax payments, and are just trying to ensure you hit the minimum payment threshold for the year, I don't see any rules about when you would have to make them, except that it would be before the final quarter's deadline, which is some time in January of the following year.