In prayer songs, we address the One God by many names. 
Each reminds us of a particular attribute which we revere.

RAGHUPATHI:  The lord (pathi) of the solar (Raghu) dynasty. 

God incarnated as Rama to deliver the world from evil. He took his birth in the Raghu dynasty - the Sun dynasty. The sun is the source of all energy; therefore, we all owe our origin and existence to the Sun. In each one of us is lodged a spark of the sun, a spark of the Divine Rama. The ultimate aim of any devout and informed Hindu is to realize this truth: that divinity is within us. It is only ignorance that stands in the way of our perceiving this truth and realizing it. What better way to dispel this darkness in our mind than to allow the brilliant light of Lord Rama of the Solar dynasty to show us the way and fill us with light and true knowledge? Let us accept Rama as our Lord: our Pathi. He was the pathi of the Raghus; we all belong to the Raghu Vamsha! Let us chant incessantly `Raghupathi Raghava Raja Ram' so that He is truly accepted by our mind as our Lord, whom we shall follow in every respect and in whom we shall merge. 
Raghava = of the Raghu dynasty; Raja Ram = King Rama; 

Pathitha = the fallen ones, sinners; those on the spiritual path who have fallen on the way; 
Paavana = One who protects, saves. 
Sita Ram = Rama, the Consort of Sita. 
In mythical terms, Sita represents the mind. When we meditate on the Lord as Sita Ram, the consort of Sita, our mind accepts Him as its Lord. With Rama as the Lord, the mentor, the guide, the Guru, we can certainly reach our spiritual goal, even though we might have fallen earlier on in our spiritual path when we disregarded the ideals established by Him in his incarnation as Rama. He saves those who have stumbled on the path and seek His help.
Sita Ram Jaya Sita Ram; Sub-ko Sun-mathi de Bhagvaan. 
Jaya means victory. The successful devotee of Lord Rama chants the glory of Rama and announces with joy the victory of Sita Ram - the victory of his mind in overcoming obstacles encountered on the spiritual path. One who has enjoyed the great spiritual Bliss wishes that every one should similarly reach the goal. He therefore entreats upon Rama to grant to everyone (Sub-ko), spiritual knowledge (sun-mathi), so that they too can share the bliss that he is experiencing. The realized ones always feel oneness with humanity as a whole and want everyone to be delivered from ignorance of spiritual truths. Having seen the glorious light and experienced true joy (Ananda), they would like others also to be with them in this kingdom of joy presided over by Rama. 

Chanting this song repeatedly in a meditative mood helps the aspiring devotee to invoke the Grace of Rama and with His help and guidance, to reach the goal of spiritual journey. It was hence that Mahatma Gandhi always chanted this as the main song in his daily prayer meetings.