The Hybrid approach, as the name implies, is a combination of the Waterfall and Agile methodologies. It takes the best parts of both Waterfall and Agile and combines them in a flexible yet structured approach that can be used across different projects.
The Hybrid methodology focuses on gathering and analyzing requirements initially - a nod to the Waterfall method. From thereon, it takes the flexibility of Agile approach with an emphasis on rapid iterations.
By combining attributes of Waterfall and Agile, the Hybrid method (sometimes called "Structured Agile") gives you the best of both worlds.
1. Increased flexibility: Past the planning stage, the Hybrid method affords you significantly increased flexibility when compared to the Waterfall method. As long as the requirements don't change substantially, you can make changes as they're requested.
2. More structured: By borrowing the initial planning phase from Waterfall, the Hybrid method addresses one of the biggest complaints about the Agile approach - lack of structure and planning. Hence, you get the "best of both worlds".
1. Requires compromise: Since you're essentially reconciling two polar opposite approaches, both sides will need to compromise on requirements and flexibility.
2. "Best of both worlds" approach robs you of the flexibility of Agile and the surefootedness of Waterfall. Any iterations you make will have to comply with the budgeting and scheduling constraints set up front.