Antoni Gaudí i Cornet was born June 25, 1852, in Reus, Catalonia (he was then christened Antonio Plácido Guillermo Gaudí i Cornet). He was the son of a coppersmith, Francesc Gaudí i Serra. He grew up. At 17 he attended the College of Sciences of Barcelona, at the Regional School of Architecture, graduating in 1878. He served in the military at the same time (this was during the Third Carlist Wars), and was sent into the field three times, although he never saw combat.
Gaudí spent some time working under other architects and designers, such as Emilio Sala Cortés, F. P. del Villar Lozano, Leandro Serrallach, Juan Salamera, and Juan Martorell. He also spent some time under Josep Fontseré, helping to design the Ciutadela Park. Under these people he learned more about design and architecture, and expanded his knowledge to include the study of equilibrium (estática gráfica), carpentry, and working with iron, ceramics, and glass.
In 1883 Gaudí started his first important independent work, Casa Vicens, in Barcelona. It was very brightly colored, inside and out, with many gingerbread-house-like trimmings. It was also very large, a mansion trying to be a small castle. It is still there, very fancy, very cool, but also rather gaudy.
It was well received, so he kept building buildings along the same lines. Casa Vicens was full of strait sharp lines, but in his later work, Gaudí became known for his sensuous curving lines. He is also known for bright colors, use of tiles, and really funky buildings. His work is classified as Art Nouveau, Gothic Revival, Neo-Gothic, or Expressionistic, or sometimes it isn't.
The best way to see what so special about Gaudí is to visit Spain, but failing that, you could do a web search on him. I'll also try to include some good URL's for you to visit.
His two most famous works are Park Guell and La Sagrada Familia. Both are in Barcelona - most of his works are in Barcelona, and all are in Spain.
Park Guell (Actually, 'Güell') was built to be a small garden city, following the garden city movement in England, which had arisen from the ideas of Sir Ebenezer Howard. The basic idea was that a city would be even better if it incorporated some countryside into it. Hence the word 'Park'. The 'Güell' comes in because this was built for Eusebi Güell. (A great many Gaudí's of works were commissioned by the Güell family).
It was intended to house 60 families, but the project didn't work out (they only sold two of the sixty plots). In 1923 it was given to the city, and is now a public park and tourist attraction. It looks something like Disney World being slowly eaten by run-away gardens. It a great example of Gaudí's work, but unfortunately it is also indescribable.
Http://www.gaudiallgaudi.com/AA010.htm has good pictures.
La Sagrada Familia (El Temple Expiatori de la Sagrada Família) is even more famous, being Barcelona's most visited tourist attraction. Gaudí started construction in 1883, and it was still unfinished at the time of his death in 1926. This was not for lack of effort - by the end of his life Gaudí was obsessed with the cathedral, and had moved on-site, the better to supervise it. It is still not finished, but they are still working on it. I could write much more, but the La Sagrada Familia node covers it pretty well, and even better, www.gaudidesigner.com/uk/sagrada-familia.html has some good pictures.
Gaudí died June 7, 1926. He was hit by a trolley while crossing the Gran Vía at Gerona. He died three days later, never having regained consciousness. He had completed 12 major works, and done a darned good job on what there was of the Sagrada Familia. He never married, and had no children.
In case I haven't made the point yet…. His stuff is really, really cool. To see it, check out these sites:
P.S. Sometimes you'll come across someone claiming that the word 'gaudy' comes from the fact that Gaudí's work is brightly colored and over-the-top. The English word gaudy has been around for hundreds of years. It is possible that Gaudí's work has influenced the modern day usage of the term, but it was not created because of him.