Daasyam stands for servent character, ie doing service as a slave. In this world we can see lot of people are working like slaves, for example warrior work as a slave to Raja, Wife do service like slave to his husband, Some father treats his children as slave. These act of serving (slave) happens due to some reasons and for some time period and later vanishes. The interlink of Jeevatma doing service (Daasyam) to Paramatma is Eternal.
This will be said as Sesha-Seshi Bhaavam , Swami-Daasa Bhaavam. This samandham (interlink) is always present, there is no start and end for this relationship. This relation is not only for indians, it is applicable for all the other country person and also for all Jeevarasis ( Animal, Plants) present in Universe. Thats what Kodhai Expresses as “Uravel Namakku Ingu Ozhikka Ozhiyaathu”. The Author tells Daasyam as two types Gunakrutham and Swarupa Prayukutham. He quotes a story for explaining this two types of Daasyam