When it is said 'Buddham Saranam Gachaami'- Buddham here means the supreme intellect within you which leads you with discrimination of right and wrong. Right- that makes your life noble and happy leading one to the state of Bliss. This aspect also embodies all the factors that makes others -the entire animate and inanimate world happy.Live harmoniously and let others live as in the creation every one has every right to lead a dharmic life.
There is another strong aspect in our life is the mind which on many an occasion succumbs to the vagaries and attractions of the world promoting the elements of 'jealosy, hatred, avariciousness, anger, wanton desire, miserliness etc (the enimical SIX that dominate ones nature deterring him from the noble and gentle nature). It strongly influences our behavior. If left unchecked it sometimes eats away the energies of humans lead them to calamity. So the possessiveness of several rulars all over thye world since centuries hence. To-days ills and randomness in the society is due to the mind alone. If a mind polluted by the enimical Six which I had given above is allowed to dominate the 'Buddhi' the world experiences the doom and the entire human race extincts. Wars prevail, animosity, hatred, selfishness, inhuman activities etc prevall. Such a mind can be controlled by the supreme commander 'Buddhi' only with its sagacity and discrimination. 'Buddhi can tame the vagaries of mind and bring it into its fold by distancing away from the enimical six. So surrender to 'Buddhi' which makes ones life like that of 'Goutama the Buddha'
Goutama or Siddhardha surrendered him-self to this intellect within him-self, distanced him-self fully away from those cruel enmical six vices and then became a 'BUDDHA' His experience made him to proclaim this message to all that 'surrender your-self to the supreme intellect or "Buddhi' (This supreme intellect in Sanskrit is termed as Buddhi)
Similarly 'Sangham Saranam Gacchami'. Surrender to the Society by involving your life for the good of the society even at the expense your own comforts in your own life.A sacrificing life for the good of the society! Only through sacrifice only ones life becomes 'IMMORTAL'. Jesus is the good example for this. Would you agree, and there are so many who sacrificfed their lives for the welfare and betterment of the society.
Last one 'Dharmam Saranam Gacchaami'. Always be righteous -so surrender to the righteous behavior and character. Dharma means the righteous behavior of humans. A human must be humane but should not embrace the characteristic behavior of animals and brutes.
These are the three Great messages given by 'Lord Buddha' from Bharata Desha (INDIA) to the human race and which were emulated by the great preachers and saints even before the christian era came into existance.