The top chart shows unadjusted weekly unemployment claims, while the bottom chart shows the seasonally adjusted numbers. Note in the top chart that there is an upward "blip" in the middle of each year (actually it occurs in the first part of every July). This surge in unemployment claims comes from the annual summer closing of auto plants. The seasonal factors take this into account by subtracting from the actual number, so if actual claims rise by the typical amount, then the seasonally adjusted number is flat. This year is likely to be different, since the auto plant closures happened for the most part a few months ago. So if the actual claims numbers don't rise by as much as expected beginning next week, then the seasonal factors will give us a seasonally adjusted decline which could last through the latter part of July.
The coming decline in seasonally adjusted claims should provide some support for the emerging notion that the economy may be picking up somewhat, now that gasoline prices have come back down and the disruption that followed in the wake of the Japanese tsunami begins to ease. In reality, of course, the market hasn't suffered as much as the April rise in adjusted claims suggested—it's simply been in a soft patch; claims have been essentially flat for the past 4-5 months. The market is already sensing improvement, in any event, and that is what is pushing equity prices and Treasury yields higher. July could see some more excitement.