Why lord Rama was called Raghunath? What is the meaning of this word and why he named so?
Raghu was one of the great renowned King of Ikshvaku dynasty. His father was Dirghabahu.
His son was Aja. Son of Aja was Dasaratha and son of Dasaratha were Rama, Lakshmana, Bharata, Shatrughna.
The son of Khatwánga was Dírghabáhu; his son was Raghu; his son was Aja; his son was Daśaratha. The god from whose navel the lotus springs became fourfold, as the four sons of Daśaratha, Ráma, Lakshmańa, Bharata, and Śatrughna, for the protection of the world. Ráma, whilst yet a boy, accompanied Viswámitra, to protect his sacrifice, and slew Tádaká. [Vishnu Purana 4.4]
Thus Raghu was the great grandfather of Lord Rama.
The name Raghu itself means fast one derived from his chariot riding abilities. He was a great heroic personality in his time. So Lord Rama got Patronymic name from him.
So, RaghuNath means Lord of the Raghus. Meaning Lord of the Dynasty of Raghu.
Just as Lord Krishna is also called Yadunath meaning Lord of Yadavas. Similarly Lord Rama is called Raghunath meaning Lord of descendant of Raghus / Lord of Ikshvaku dynasty.