Here is a bit more detail for those who are interested.

First, I would strongly recommend reading this excellent feature in TIME by George Church, “Anatomy of a Disaster.”

The American hunt for Aidid peaked on October 3-4, 1993 in the Battle of Mogadishu, which resulted from an effort to seize two of Aidid’s high ranking associates. As you know from the film, it did not go well. 18 American deaths, 73 wounded, and one captured pilot. What you don’t see in the film is what Americans saw on their TVs over the next week, which changed American policy in Somalia:

What they did see were ghastly photos of a white body, naked except for green underwear -- apparently the corpse of a downed helicopter crewman -- being dragged through the street while Somalis kicked and stamped at him, plus TV footage of a terrified helicopter pilot, Michael Durant, being questioned by Somali captors.

In fact, the Somali captors made a video of Durant appealing to the American public to leave Somalia:

"When you don't live here, you can't understand what's going on in this country. We Americans have tried to help. But at one point things turned bad."

And that is how Aidid won his victory:

If Aidid's purpose was to convince the American public of the same thing, he succeeded. Thousands of horrified citizens wrote and phoned the offices of congressional representatives, posing angry questions: What was the U.S. doing in Somalia?

Less than one week later, President Clinton addressed the nation and announced withdrawal:

Clinton intends to downgrade, though not officially call off, the hunt for Aidid.

…

Clinton and Christopher also sent pleas to African leaders to join in promoting a peaceful settlement. Whether or not these efforts work, though, the American troops will be out no later than March 31. Period.

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Supposedly, U.N. troops from other nations will remain; in fact, the White House sent messages to 30 countries asking them to increase their forces to take over from the Americans (fat chance).

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The early-departure policy had one immediate success: it calmed the revolt in Congress. Whatever doubts they might retain, lawmakers generally welcomed a firm deadline for withdrawal -- and what they took as a sort of declaration of independence from the U.N. and Boutros-Ghali.

The UN didn’t last much longer. On 24 April 1994, Boutros-Ghali admitted defeat and declared the U.N. Mission was over. All UN soldiers eventually withdrew from the country on March 3, 1995.

So Aidid seemed to have escaped the justice of the world community. But alas, he did come to a bloody end nonetheless a year later due to a bullet wound sustained during fighting with the forces of a rival warlord, as reported on August 2, 1996:

MOGADISHU, Somalia: Somalia's most infamous warlord, General Mohamed Farrah Aidid, died Thursday of an apparent heart attack, after being injured by a bullet last week. Aidid and his armed cadre resisted attempts by the United Nations and United States to restore civil government in the anarchic nation, forcing the U.S. to retreat ingloriously in March of 1994 and the U.N. a year later. Aidid's death has been confirmed by his own radio station, which declared a 30-day period of mourning…Since news of Aidid's wounding circulated last week, a strange calm has fallen over the country and even Mogadishu, usually the site of the most intense fighting, is quiet…The general's death leaves a power vacuum in central Somalia…

And as /u/DBHT14 noted, that power vacuum did not go well either.

He was killed less than a year later in 1996 during a clash with a breakaway splinter faction of his larger group.

Somalia remains a failed state today and a haven for both secular organized gangs, groups driven to piracy, and Islamic extremists.

So the UN withdrew in 1995, the Battle of Mogadishu was in 1993, my mistake for just looking at the dates!

Something I can talk about! Mohammed Farah Aidid retained control of the United Somali Congress until his death in 1996. However, that's just the start of an interesting story. So the UNITAF mission to capture Mohammed Farah Aidid (on which Black Hawk Down is based) had only one Somali translator. This was not a fluke with the mission planning, but all the was available - there was only one Somali translator in the whole marine corps. The translator's name was Hussein Mohammed Farah Aidid. If that name sounds familiar to you, it should, because he was the son of Mohammed Farah Aidid; the main target of the mission. Hussein was raised in Texas, was a registered Republican, and a member if the US marine corps. Now following the failure of this mission and his discharge from the corps, Hussein returned to Somalia and following his father's death, took over for him as the leader of the Somali National Alliance. I just find it so funny to think that in Somalia right now there is a registered Republican, former marine warlord.

Source: Joseph Wojciechowski, "Foreign Influence on Warlordism in Somalia", The Journal of Politics and International Relations, 2013.