In addition to the literal meaning of this term -- someone buying up all a company's shares, a company buying another company, or what have you -- a "buyout" can also refer to a social event in the corporate world.
If an executive leaves one organization for another in pursuit of more money or a more prestigious job title, and if there is no bad blood with the original company, the departing executive will throw a party known as a "buyout." Basically an invitation will be sent around to everyone in the company inviting them to a nearby pub for drinks. The person who's leaving will pick up the tab at the end of the night.
As you can imagine, this gets expensive. But in certain industries, the assumption is always that you're leaving something good for something even better, which means that it's "only polite" to do a favour for the people left behind. It's a little like the unspoken rule among gamblers that someone who wins big buys a couple rounds for the table before leaving for the night.
Ironically, this tendency has only intensified in the current economic climate: a fierce defensiveness about joblessness and recession leads to an even more frantic desire to spend lavish amounts of money on frivolities.