The reason why they chose 'Buratha'.

A new massacre has struck Baghdad when three suicide bombers attacked the Buratha mosque in Baghdad this afternoon. "More than 70 people were killed and more than 150 were injured" a doctor from Baghdad's medical city told me in a phone call.

A closer look at the targeted mosque makes me think that the ramifications of this massacre can possibly be much worse than the immediate death and pain this terror attack brought, the Buratha mosque is not an ordinary mosque, it has a special religious value for Shia Iraqis as it's thought to be one of the places where Imam Ali stayed and prayed. But that's not the most important thing because this mosque is of considerable political significance, the preacher in this mosque is Jalal Addin al-Sagheer, a cleric from the SCIRI who was the first SCIRI member to publicly urge Ibrahim al-Jafari to withdraw his nomination for office.
This mosque is one of the headquarters of the SCIRI and its clerical wing in Baghdad, even that Abdul Aziz al-Hakeem's son Ammar al-Hakkem preaches occasionally in this mosque when sheikh Jalal is not available.

A military confrontation between the Sadr militias and the American (and possibly Iraqi) army is imminent and it's the Sadrists themselves who are pushing in this direction and preparing their forces for a battle they want to have to disrupt the political process and drag Iraq into an irreversible state of civil war.
There are powers in the region that want this to happen, primarily Syria and Iran but I think they realized that a Sadr Vs. US battle is not enough and can only result in a big defeat for Sadr without reaching their desired objective of ruining Iraq.
So, it is logical to think that Iran and Syria would try to drag as many Iraqi parties as possible into this battle and the first candidate they would choose would be the SCIRI, the powerful Shia party that is not getting along well with Sadr and has recently sided with the Kurds, Sunni and secular powers in calling for Jafari to step away and even considering forming a united political front with them.
Another possible theory is that this attack is a warning message to the SCIRI that they must stay friends with Sadr, support Jafari and abort any plan to form a unity government with the Kurds, Sunni and secular parties.
If either theory is correct, the attack is aimed at stopping Iraq from having a government and prolonging the instability for as long as possible.

Let's also take a look at the planning for the attack that is very well studied too, the suicide bombers did not start striking during Friday prayers when the place is usually heavily guarded and security personnel are at high alert but the first strike came more than 15 minutes later when an attack is less expected and after guards felt they accomplished their mission in protecting the worshippers during the main ceremony to be followed by the other two bombings that took advantage of the state of panic created by the first bombing. This in addition to the use of disguise has of course made the breach easier to make.

The attack was no doubt carried out by al-Qaeda but the target was chosen from the powers across the borders.