If there was one period that exemplified the phenomenon of Lisztomania, it would be the years from 1839 to 1847. These years are often referred to as his Glanzzeit period, his 'Time of Splendor'. This was essentially Liszt's second career. He had been quite popular in his teens, and gained an impressive level of notoriety for one so young. But after his father's death in 1827 he stopped playing in public for years. Finally, in 1837 he was convinced to travel to Paris to take part in a piano duel with the famous Sigismund Thalberg. While there, he learned of devastating floods of the Pest district of Budapest, in his birth country of Hungary.
Liszt immediately undertook a series of relief concerts to raise money for those affected. He raised more for the victims of the flooding than any other private donor, and he cemented his status as a national hero of Hungary. This was only the beginning; he subsequently started to tour all over Europe and beyond, giving over a thousand performances in numerous cities: Dublin, Madrid, Istanbul, Odessa, Moscow, and everywhere in between. This is when Lisztomania truly began.
Beatlemania was named after Lisztomania (the term was coined in 1844 by Heinrich Heine), and Lisztomania may actually have been the more extreme of the two. Liszt was mobbed by fans who would try to grab souvenirs such as gloves and handkerchiefs and even cut locks of his hair. Admirers were recorded as stealing dregs from his coffee cups and wearing them in vials around their necks, and one wealthy lady had one of his discarded cigar stubs mounted in a locket surrounded by diamonds. His broken piano strings were in great demand for making bracelets.
There are an number of things that made Liszt special. New piano-making techniques included innovations such as expanding the keyboard from 5.5 to 7 octaves, new techniques in string manufacture allowing for greater dynamic range, improvements to allow a lighter touch to produce a stronger sound, and for successive, repetitive notes to be produced more rapidly. Liszt took advantage of these developments to do things that had not been seen before, and his skill at integrating new developments into his music convinced the famous piano maker and innovator Sebastien Erard to give Liszt his newest and best piano -- keeping Liszt ahead of the curve in both technology and skill.
Liszt also set up his concerts differently than was the norm at that time. He was up on the stage for the entire concert, at a time when concerts usually had multiple headliners. He commanded entire concert halls, instead of the smaller venues that other solo players would usually seek out. To maximize the volume of his piano he was the first to place the piano at a right-angle to the audience, leaving the lid open to reflect the sound across the concert hall. This also had the effect of presenting his profile to the audience, improving their view of the artist.
Of course, his concerts were quite special even without the new developments; he would memorize his entire program, and play pieces from Bach, Beethoven, Schubert, Wagner and Berlioz in addition to his own pieces. Not only were his own pieces technically complex and disturbingly avant-garde, they were also fun and in some ways very accessible, incorporating both popular and traditional folk tunes in his pieces.
Lisztomania came to an end in 1848, when after eight years of touring he fell in love with the Polish Princess Carolyn of Sayn-Wittgenstein. Although she was already married (to a prince!), she chose to run away with Liszt, and they moved to Weimar, Germany, where he had been offered the position of kapellmeister. Liszt continued to distinguish himself as a musician, composer, and all around cool guy, but without the boon of constant touring he quickly slid from superstardom.