The Blessing Star was a crystal or jewel the First Doctor and Susan obtained on the planet Tacunda. It could fundamentally alter the laws of probability around its owner, giving them extraordinary good luck.
In the Doctor's case, it made it more likely that he would be able to pilot his TARDIS to 20th century Earth. It also had the effect of burning out the navigational system and stranding the travellers in 1963 London. At some point after Susan enrolled at Coal Hill School, she took the Star to school, hoping it would help her fit in. However, it only turned her into more of an oddity by making her unnaturally lucky. She cursed the object and buried it in I.M. Foreman's junkyard. After months of trying to effect repairs, the Doctor was approached one night by Ian Chesterton and Barbara Wright, who pushed their way into the TARDIS. He subsequently dematerialised the TARDIS in a hurry, leaving the Blessing Star behind.
Later, after Foreman's liquidation of the site, Joseph Galloway, a rag and bone man, discovered the Star, still where Susan had buried it. He retained the device and immediately felt his luck shifting. He got married, won substantial sums gambling, and even realised that the items he found whilst scavenging were increasingly valuable. One day, he began to watch the 1966 World Cup and the jewel started to respond to his fervent wish for England's victory over Germany. As he watched the final, the Doctor, fresh from his victory over WOTAN, (TV: The War Machines) found him. The Time Lord had been tracking down the Star so as to tie up loose ends from his last visit to England. To his dismay, he found the Star too late. By then, the Star had started to overload, taking in not just Galloway's wishes, but those of people all over England. The Star allowed England to make a very close shot into the German goal, but no more. It exploded, overwhelmed by the hopes of an entire nation. England went on to win, but without any further help from the Star.