In the first two months of the hurricane season, i.e. up to the end of July, typically only one tropical cyclone has occurred in the north Atlantic Basin, but in the last decade, an average of three named storms have already occurred by this point. Also in the last decade, there has been about a fifty percent chance of a hurricane forming before July 31.
Tropical Depression One has been the only storm of the season, and it formed before the season started, in May, making it a preseason storm. Since then, hardly any activity has occurred and no cyclones have formed. The very opposite of this has happened in the East Pacific Basin, where, after a late start, five tropical cyclones, four of them named, and two of them hurricanes formed before July 31.
Some potential for tropical cyclone formation was present in June, and a fair amount of tropical waves came and dissipated during that time. However, an El Nino event (see here) that had been building for months reached strength in early July, stopping anything from forming. The current prediction is for a near average hurricane season with 11 named storms. However, the current trend may end in a below average season, the first since 2006, and before that, 1997. Both of these seasons' source of inactivity was an El Nino as well.
Despite this, there are exceptions. In 2004, no storms formed until August 1, which is a very late start. However, the 2004 season went on to have 15 named storms, with 9 hurricanes and 6 major hurricanes, along with over 3,100 fatalities, making it one of the most damaging seasons ever.
Hurricane activity is very unpredictable, and a lot may happen between the end of July, and the end of November which marks the end of the hurricane season.
Sources: National Hurricane Center, and wikipedia (which got its information from the National Hurricane Center)