Juan Cole over at Informed Comment explains it best. The one point I would like to add however is that explosives as incredibly powerful as those used in Sundays carnage are not easily available. When a conventional explosion of this size occurs you have to wonder if there is governmental involvement. Since it was a Sunni attack against the Shia dominated ministries this point the finger at Syrian or even Saudi involvement.
The particular ministries that were struck may be significant, since Iraq operates on a spoils system and ministries tend to be dominated by political parties and ethnic groups. The Minister of Public Works is Riyadh Gharib, a prominent member of the Islamic Supreme Council of Iraq, which is close to the clerics in Tehran. Public Works as a ministry would thus have a lot of ISCI party members as employees and it is also a huge source of political patronage. Baathists or Sunni extremists would have every reason to hit it.
The Ministry of Justice had been less politicized, but from 2007 was in the control of the Shiite United Iraqi Alliance. The Minister of Justice from last February is Judge Dara Nur al-Din, an independent Kurd. He had been a member of the Interim Governing Council under Paul Bremer, for which some groups in Iraq may not have forgiven him. The ministry of justice also oversees court cases and executions, including of prominent Baathists, executions that Nur al-Din has defended, and which have angered the anti-government guerrillas.
As for the Baghdad Provincial government (it is both a province and a city), it has been dominated since the January, 2009, provincial elections by the State of Law coalition of Prime Minister Nuri al-Maliki, the leading element of which is the Shiite Islamic Mission Party (Da'wa).
So if the guerrillas who set these bombs were trying to kill party cadres attached to ministries, you'd have to conclude they were trying to kill those of the ruling Shiite religious parties, and also to take revenge on the new regime for the Ministry of Justice's executions of Baathists and Sunnis.
The attacks inevitably had implications for the January, 2010, parliamentary elections, insofar as they make Prime Minister Nuri al-Maliki and his ascendant Islamic Mission Party look incompetent in providing security. Since al-Maliki has done a fair job of restoring security to cities such as Basra, this success is a campaign talking point for him, which the guerrillas are attempting to deflect.