For those of you who have never had the privilege to go to a classical music concert with your local symphony orchestra, I would recommend going when one of the pieces on the program is a concerto. A concerto is a piece with the symphony orchestra and a soloist [of an instrument] who stands or sits in the front, closest to the audience. So, a piano concerto would have a pianist in front of the orchestra. A violin concerto would have a solo violinist standing in front of the orchestra, etc.
There are also double and triple concertos which would involve more than one soloist, and they would be in the front of the orchestra facing each other. For example, in Beethoven’s great triple concerto there is a solo violinist, solo cellist and solo pianist in front of the orchestra:

A concerto, literally means contest or competition. There will be no winners or losers in this contest but you will at times have the orchestra taking the lead, and at other times the soloist will take charge. Most of the time, though, the soloist and orchestra work together to make some exciting music. It is wonderful to hear the play between the orchestra and soloist. It is also fun to watch the conductor, while conducting for the entire orchestra, making eye contact with the soloist to make sure they are both on the same page.
The concertos are somewhat like symphonies, with the addition of a soloist with the orchestra. But while a classical symphony usually has 4 movements, a classical concerto will almost always have 3 movements [usually in the form of fast, slow, fast]. Also, in a concerto something that you will have that you will not have in a symphony is the cadenza. A cadenza is when the entire orchestra will put their instruments in non-playing positions, and the soloist performs, by himself, a segment that is meant to show off the virtuosity of the soloist.
One more thing you will notice about the concerto is that for the most part [but not always] the soloist will play the piece by memory, without the music. That is in a solo concerto. For double and triple concertos, I think because of tradition, most of the time the solo players will have the written music before them.
Without further ado, here are examples of the concerto for different instruments: Rachmaninoff’s thrilling, dramatic and extremely virtuosic piano concerto #3; Tchaikovsky’s great and exciting violin concerto; Mozart’s sublime clarinet concerto, Hummel’s electric trumpet concerto, and the previous mentioned epic Triple Concerto by Ludwig Van Beethoven. Please, turn up the volume [especially for the trumpet concerto] and enjoy these great concertos!
S. Rachmaninoff: Piano Concerto #3 in D minor:
J.N. Hummel: Trumpet Concerto in E Major:
W.A. Mozart: Clarinet Concerto in A Major:
P.I. Tchaikovsky: Violin Concerto in D Major:
L.V. Beethoven: Concerto for Violin, Cello, and Piano in C Major:
Bravo, Concerto!