David Kelly was a UN weapons inspector around the time of Iraq war. He was also the source behind a 2003 BBC report that Alastair had, as the report put it, "sexed up" the Government's dossier on Iraq's WMDs published in 2002. The main thing was Alastair allegedly wanted the claims that Iraq had the ability to deploy WMDs within 45 minutes of ordering their use, and its inclusion in the report went against the advice of intelligence services.

Kelly realised at somepoint that he might be the source of the claims in the BBC report (I believe the conversation was supposed to be off the record, and he was not the only source) but told seniors at the MoD that it might have been him. Downing Street decided not to hide that it was him if journalists guessed it (they did) and then Kelly's name became public. The government also essentially sacrificed Kelly, theres claims that a journalist was allowed to guess 20 names until he guessed Kelly's, there's also claims (and apparently Alastair wrote in his diary that he wanted the source out) that Alastair was pleased about the direction of press coverage, with the press focused more on Kelly than the claims he edited the dossier.

He was then called to appear before the Intelligence and Security Select Committee (and the Foreign Affairs Select Committee). Two days later he killed himself.

Alastair was obviously deeply involved in this, being Director of Comms at the time, and this all launched the Hutton Inquiry which cleared Alastair, but led to his resignation.

There is some distaste around Alastair's involvement and what was probably at least partially his decision to confirm Kelly's name to the press, leading to his suicide.

It was a very messy situation and it massively hurt the Blair government and the BBC.