Graha means grasp/grip or one who grasps/grips. The nine grahas are the nine celestial bodies that take our consciousness into their grip when the right times comes (based on certain celestial formulas). They create environments and situations in our life to create certain states of mind.
For removing obstructions in material and spiritual aspects of life, we propitiate grahas. If a graha is pleased with our propitiation, it will not create situations that create a certain state of mind that may be ahindrance to our material and spiritual progress. To propitiate grahas, one can read their Veda mantras or kavachas or stotras.
Veda mantras are very powerful. But they work slowly (mainly because most people do not know these days how to chant/experience them perfectly). Big counts are needed. When you persist with a Veda mantra, it first removes the obstacles caused by an aspect of Brahman represented by the deity of the mantra and eventually creates a perfect understanding of that aspect of Brahman. All Veda mantras are eventually for a perfect understanding of various aspects of self only.
Sun is the soul. Moon is the mind. Mars is the energy/initiative/drive within. Mercury is the flexibility, ability to learn and adapt. Jupiter is the wisdom, discretion and judgment within a person. Venus is the spirit of being happy. Saturn is the spirit of working hard and going through austerities. Rahu is the spirit of breaking the barriers,innovating and reaching for the unknown. Ketu is the spirit of perfect detachment
with everything. Veda mantra of a graha, when chanted for a long time, removes the obstacles thrown by that planet based on dasa and gochara and eventually gives a perfect understanding of the aspect of self represented by the planet (as mentioned above).
Kavachas of grahas, when chanted many times, create an unseen protective shield around the person. Kavachas can be used for overcoming physical ailments, health troubles, prayogas etc. Stotras are meant for pure bhakti maarga. They praise various qualities of a graha. In addition, there are various beeja mantras also.
According to Parasara Maharshi who taught "Brihat Paaraasara Horaa Saastram", the greatest classic on Jyotisha, grahas are Vishnu's avataras. They comprise of the energies of various incarnations of Vishnu. Ramachandra's energy is Sun. Krishna's energy is Moon. Nrisimha's energy is Mars. Buddha's energy is Mercury. Vaamana's energy is Jupiter. Parasu Raama's energy is Venus. Koorma's energy is Saturn.
Varaha's energy is Rahu. Matsya's energy is Ketu. Apart of doing japam with these graha mantras/kavachas/stotras, one can also do a homam. Homam is always a better avenue than japam and others. In navagraha homam, you invoke the nine grahas in fire and offer oblations with their Veda mantras several times. It is also possible to do a homam for just one graha.
