The intuitive answer to me would be to "emphasize" something. This explanation seems different from others I've seen, however, that say it means to "finish something". Help on this?
The idiom does have a different meaning from "emphasize".
draw a line under something
if you draw a line under something, it is finished and you do not think about it again: Let's draw a line under the whole episode and try to continue our work in a more positive frame of mind.
It's an expression which originated as a term used by Accountants, in preparing the accounts -- especially the profit-and-loss account -- for any trading business.
Drawing a line under it is literally what the Accountant does, on the printed page, to rule-off the end of one trading period. At the end of the trading year it's traditional to draw a line across the page to mark the end of a trading period, and that marks the point up to which the trading accounts of the business are prepared for that period.
By literally drawing a line under the end of the year's trading, it physically separates one trading period from the next: the annual accounts are then prepared up to the marked point, with any later income or outgoings assigned to the following period.
Over time, it's become customary to use this expression in far wider contexts than simply business accounts, and the expression now denotes any situation where someone wishes to speak of making a fresh start.
In accountancy, each new annual trading period represented a fresh start for the business, whether the previous 12 months had been good or bad for it. This concept of ruling off events in the past and starting again is nowadays a form of common usage in a wide range of activities, many entirely unconnected to business finance.