The campaign for Arma 3 will be released post-launch as three free downloadable episodes. The first one is called Survive, and will be available about a month after release. The other two, Adapt and Win, are coming sometime afterwards.
The announcement acknowledges a troubled development, and suggests that this decision was made to get the core sandbox out to players and modders as soon as possible. Specific release details haven't been announced, but it's said to be releasing in Q3.
"This was not a decision we made lightly," said project lead Joris-Jan van't Land, in the announcement. "As game creators, we love developing and playing through campaigns so, to those awaiting ours, we say: sorry for the delay. After talking a lot about a focus on quality over the last year, it simply did not feel right to compromise now. Rather than pushing back the entire game, we launch this year with an awesome package--a splendid kick off for the Arma 3 experience."
A more detailed blog post gives more detail on the studio's work so far, and what went into this decision. It says that unexpected events (likely referring to its strange staff arrest in Greece) put a strain on development. Meanwhile, business considerations are keeping the studio from just delaying the full game altogether. Bohemia considers the the main release as a "platform," though, and hopes fans will be satisfied with the open world while they wait for the campaign.