As part of today’s massive rollout of new Pokémon GO features, players will be able to earn one Stamp per day by completing at least one Field Research task, and when you obtain seven stamps, you can achieve a Research Breakthrough to receive even greater rewards; you may even have an encounter with a Legendary Pokémon! There are two different types of research you can contribute to: Field Research and Special Research. Gather Field Research tasks by spinning nearby PokéStops, which will give you objectives that include discovering and catching certain Pokémon or engaging with battles, among other things. Special Research may be requested by Professor Willow himself. According to The Pokémon Company, the Search for Mew Special Research can be challenged once by each player. In addition, Pokémon GO players must be a level 5 standing or above in order to go on the Search for Mew quest.
Source: Official Pokémon GO website