The 'Brown Revolution' is a play on the Green Revolution; while the Green Revolution focused on quickly increasing crop yields around the world, the Brown Revolution is a focus on sustainable, long term crop production, with a large focus on soil health.
A large portion of the farmers in the world are small-scale, very low income, and work primarily to feed themselves and their families; this group consists of about 2 billion people. The Green Revolution has not been much help to these farmers, as paying for seeds is not a feasible option, and using seeds just because they grow great in Mexico is a suicidal option. Nitrogen fertilizer and predictable irrigation schedules are also off the table. For these farmers, often the best thing they can do to make their farms more productive is to focus on maintaining a set of crops that maintain healthy soil.
A smaller, but still large number of farmers are doing pretty good with Green Revolution, and are making good money selling crops at market. However, decades of relying on heavy fertilization and heavy irrigation have resulted in very poor soils that are entirely dependent on outside fertilization, or in some cases, are so over-fertilized that taking a year off from adding fertilizer results in increased yields.
The best thing for these farms is... complex, dependent on local growing conditions, and limited by market forces, weather, wars, and dozens of other factors. However, often the best course of action for increasing long term productivity is to look at local conditions and determine what is best for keeping the soil healthy without expensive inputs (i.e., irrigation systems and artificial fertilizer), focusing on local crops and traditional farming systems, and active experimentation and information sharing in local communities.
The Brown Revolution tends to swing hard between "keep your soil healthy" and "look how effective the traditional systems turned out to be!", but the revolution part is the experimentation and information sharing aspects. While many sustenance farmers in Africa know that planting Acacia tress in their fields make their plants grow better, what they need for keeping the soil healthy now is which species of beans will grow best locally. However, there are some good practices that can be used in many places around the world; for example, beans and corn work well together, and where farmers use zai pits, targeted fertilization with compost tends to work well.
The central goal of the Brown Revolution is help small-scale, low-income farmers become self-supporting, regularly producing enough to keep their families well-fed, and hopefully have enough extra to sell some at market. Healthy farms should result in healthy families and healthy communities, and be the next small step out of poverty for a large portion of the world's population.