Overall, NASA's funding is increasing by a small amount. More funding will go into Earth Science and Climate Change satellites, and more focus will go to research and development efforts. The big changes, however, are primarily in the human space program.
Obama has extended the life of the International Space Station (ISS) to 2020 (which is good - I wrote a white paper last year arguing why), and is providing significant funding ($6B over the next five years) to help stimulate the development of commercial companies building rockets that will be able to fly to the ISS. Development of commercial human space launch is a growing area of the space industry, and most people are supportive and excited about these developments.
However, Obama is canceling the Constellation program, which began five years ago, and which included plans for NASA to build a new human spaceflight capsule (Orion), a new launcher to go to the space station in low Earth orbit (Ares I), and a 'heavy launch' vehicle to take us to the Moon and eventually to Mars (Ares V). That means that NASA will be fully reliant on commercial space companies to provide an American option for getting to space - NASA will no longer own its own rocket able to go to low earth orbit or the space station.
The budget does include research and development funding to look at new technologies for heavy launch vehicles - the type of vehicle we need to get beyond low Earth orbit to the Moon or Mars. However, the budget doesn't identify any particular vehicle that will be built and doesn't have any suggestion of a destination (Moon, Mars, Asteroid, etc.) or timeline for future human exploration.
With all this change, it's been an exciting and controversial time, as the space community comes to grips with this new proposal. However, there are still a few unanswered questions.
First, no one knows yet what Congress will do, and unless they approve the Presidents budget, and actually authorize and appropriate funds to NASA, there's no way to be sure that these changes will stick. In fact, based on some press releases and quotes in the news, it's likely that the Congressmen in Florida, Texas, Alabama, and other states with NASA centers are not going to allow a big NASA program like Constellation to be cut without a fight.
Since there isn't much detail on the long-term vision for NASA - time-tables, destinations, vehicles to go beyond low Earth orbit - there's a question of how sustainable the plan will be. It might be easier to cut funding or change direction in coming years since there isn't a clear goal, and this uncertainty could make it difficult for NASA to make progress.
Finally, even if the President's budget goes through as is, there is still some question about whether Commercial companies can deliver. Though many (including myself) hope that these companies will prove successful very quickly, and think they probably will, they've yet to have a successful unmanned launch, let alone a manned launch. Relying on commercial companies completely is a gamble, because NASA will not have it's own vehicle to fall back on, and furthermore, it will no longer have the expertise and the facilities to build these rockets, since these people and facilities can't be sustained when they have no project to work on.