Ashwamedha Yajna was done to empower your kingdom and glory, so the ashwa(Horse) was Sacrafice(send Free to go anywhere). And what so ever the land the Horse was going to cover would be considered as a Integral part of the Kingdom of the person/King who had performed the ritual of Ashwamedha Yajna(Yudhisther and Pariksheet had done for the said cause). If any king/person will stop the horse or refuse to accept the kingship of the King(who performed the Ashwamedha yajna) need to fight for that(Just like Luv-Kush fought against the army of Lord Rama).
It was considered if anyone does 100 Ashwamedha Yajna, he would be considered as Indra, as Indra was the King of Gods,and was the king of entire Swarga. Hence if anyone will perform the Ashwamedh yajna 100 time will naturally cover all the earth, and hence will be considered as Indra, as he would be the only King of the Kings on the Earth.
Ashwamedha Yajna was also done if anyone thinks he had committed any big Mistake or sin in his life and now want to do the Penanace for that(Lord Rama has done the Ashwamedha yajna to do the Penance for killing a women(Strihattya of Tarka) and a Bramhmin()Bramhahatya of Ravana).