A development deal is an arrangement made between a movie studio and an independent production company (sometimes even just an independent producer). Under the deal, the studio or other financier agrees to pay the costs of developing on or more projects to the point where they are ready to be financed and go into production.
Development is the first stage of any film project and involves turning the idea into a project which can be given the green light. During development, the producer is doing things like acquiring options and possibly rights to underlying materials (e.g. a book), working with the writer to develop the script, talking with agents about key cast, looking for a director (if one isn’t already on board), talking with financiers about the likely scope of the project, etc.
Development money is the riskiest investment in the film industry as many films which are developed never go into production; meaning that the money is lost. So in cases where someone has a “development deal” with a studio, this usually means they have been engaged to develop a slate of projects (rather than just one). This spreads the studio’s risk – it’s more likely that at least one of the projects from the slate goes into production – and also brings down the overall cost because certain development expenses (e.g. production office overheads) are once-offs which can be applied against the entire slate rather than a single project.
Studio development deals tend to be very difficult to come by for filmmakers who do not have a track record. Often, new and independent filmmakers must finance this stage of a project themselves (although outside of the US, many national film commissions operate some kind of scheme to help locally filmmakers develop their projects).