What do they mean by “bottom line” and why did US IRS turned back 810 millions to IBM? and what do they mean by “unspecified “ layoffs? In the quarter ended in March, IBM’s revenues rose by 5.1 percent to \$19.1 billion, and its gross profits were up by 6.1 percent to \$8.25 billion. There were a whole bunch of things that affected the bottom line in the quarter, including a settlement of two audits by the US Internal Revenue Service that gave it back \$810 million, but IBM then took \$610 million in restructuring charges for unspecified layoffs. The company also took some charges – IBM’s chief financial officer, Jim Cavanaugh, did not say how much – that pushed its overall systems business into the red ink.

Why did US IRS gave 810 to IBM? and what do they mean by saying bottom line?
As regards your second question,
"Bottom line" is a descriptive term for profits/losses, visualizing that when we calculate whether we had profit or loss,  we start writing revenues then expenses and at the end we have a line that tells us the difference between the two. But since it is the "last line" it is also at the "bottom" of what we have written, hence "bottom line".  

Sometimes it is also used figuratively to indicate the "end result" of something other than financial activity, especially with an intent to brush away reasons and excuses why something did not happen or happened inadequately.