As ‘Ashva‘ is the symbol of mobility , valour and strength and the ‘medha’ is the symbol of supreme wisdom and intelligence , the natural meaning of ‘ Ashvamedha ‘ can be taken as "the combination of the valour and strength and illumined power of intellect ". By assuming ‘Ashva‘ as the symbol of muscle power and 'medha' as the symbol of mental power, their combination makes a sacred and great deed of yajna.
Detailed description of the following experiments of yajna is found in ancient scriptures:the Bajpeya yajna for increasing the good tendencies in the society; Rajsuya yajna for establishing the political order; Ashvamedha yajna for making the entire nation united, powerful and progressive; etc. Ashvamedha [horse sacrifice] has been called best among these yajnas- the king of yajnas.
Truly nation is Ashvamedha, hence perform yajna to integrate , to unite the nation through the medium of Ashvamedha. This usage has a hidden meaning - perform yajna with valour and intellect .