The dissidents think the "old" ira and Sinn Fienn have given up the fight, and aren't properly representing the wishes of republicans any more or doing enough to ensure a united Ireland. So they're taking matters into their own hands and using the old terrorist/ fear tactics to try to get their own way. Which won't work this time around, because they don't have the support they did before, and can't keep up with the new intelligence technology. As pp's have said, the anniversary of the Easter rising has inflamed the situation, "100 years and Britain still has the North". Senior republican politicians know who they are, but can't name them. I just hope the recent arms find wasn't the tip of the iceberg. There have some been some awful "punishment" killings recently, over drug dealing activity, which is frowned on by the dissidents. In the protestant area, the paramilitaries (uvf, uda etc) and drugs go hand in hand (this has caused many turf wars over the years). The two sides have very different attitudes to it (both extreme in their own way).
Good video about the Southern (and much tamer compared to their Northern counterparts) dissidents.
Tourists should be fine, I don't think the dissidents would target "shared space" areas, and risk harming one of their own by mistake, more likely to target protestant areas (where tourists are much less likely to go), or members of the security forces/psni/etc, as with Adrian Ismay, the prison officer who was murdered by the new ira in March. They put a bomb under his van outside his home in the East of the city 
Lived in Belfast all my life, and love it despite the obvious downsides to life here. We're generally a friendly, welcoming wee city. I haven't noticed any increased security either.