The Holy Grail is a religious icon in Christianity, as well as several other Earth religions. It is the cup used by Jesus at the Last Supper, and many believe it to possess miraculous powers. Other names used to apply to the cup or other vessels like it are "Vessel of Regeneration" or even "Cup of the Goddess" (the latter obviously not being a Christian reference).
Aldous Gajic spent half of his adult life searching all the known worlds for the Grail, but was unable to find it. He inherited this position from another man who himself had searched in vain his entire life. Neither the Minbari Federation nor the Centauri Republic had any knowledge of it (nor presumably did the Narn Regime). Aldous died in 2258 on Babylon 5. His search did not end as Jinxo took up his quest upon Aldous' death.