It means that when you play a "C" on a piano ( also called concert C, the note produced then the trumpet is playing the same "C" is actually B flat i.e. one tone lower. A lot of other instruments, mainly wind and brass are in either B flat or E flat. The next question i.e. why do they do this - I don't know the answer to

Every musical instrument has its own perspective "A" note which is 440Hz for that particular instrument. The size, shape, and design of the instrument changes the color and pitch of the tone. To the human ear, each type of instrument will have a different sounding pitch even though technically when its playing the note "A" its being played at 440Hz. The key of an instrument (whether B-flat, E-flat or otherwise) was originally based on the abilty to play a range of notes on a particular sheet of music. Around the mid to late 1700's or so classical music composers would write music in various key signatures which made some songs difficult to play. To remedy the problem the average orchestra trumpet player would have 3 or 4 trumpets (that played in different keys) that were designed to make playing a particular composition easier. The composition could be transposed to match the specifications of the instrument and what was once a difficult fingering situation now became much easier. Most of the music composed today falls comfortably in the range of the B flat trumpet and that is part of the reason why its so commonly used.

When an instrument is listed with a pitch name (e.g. Trumpet in Bb), it means that when they finger and play a C, that note (i.e. Bb) is actually produced. The direction and magnitude of displacement varies per instrument. A B-flat trumpet plays a note one whole tone lower than it is written. These distinctions are based on the assumption that an A is defined at 440 hz (and its multiples by powers of two), or thereabouts depending on the model and its tuning.

The reason instruments are pitched differently (i.e. Horn in F, Trumpet in Bb, Saxophone in Eb) is for the same reason that we have different clefs. The range of a french horn is such that if written in C, it would use too many ledger lines below the staff. For this reason, the instrument's music has been transposed up a fourth to eliminate many of the ledger lines.

If you were in band, you might know that all of your instruments are not in the same key. There are concert instruments, b-flat, e-flat, f-horns, A piece may be in C Concert Major ( Tubas, flutes, bells, xylophones). So that makes a B-flat horn (most clarinets, most trumpets, Tenor Saxophone) one whole step higher than the concert major key. If the concert major key was in B-Major that would make your B-flat horn in C# major key

I'll tell you what it means. It means that when you play a C on the trumpet, it sounds a B flat on the piano.

Every brass instrument has a harmonic series - the notes you can play without depressing any of the valves. Depending on the length of tubing the harmonic series can be based on the key of B-flat, C, D or E-flat (trumpets), F (horns). It is conventional for trumpet music to be written in the transposed key, so that a trumpeter playing a B-flat trumpet, seeing a written C, would sound B-flat. This is a hangover from the days of natural trumpets which had no valves and could play only the harmonic series: most composers wrote the parts in C major, but expected them to sound in D or E-flat or B-flat as indicated at the start of the music. For some strange reason, most modern trombones are B-flat instruments but their parts are notated as though they were pitched in C. Similarly, most Handel trumpet parts are written in D major (2 sharps), again at variance with the common convention. All trumpet players of any reasonable standard (from good amateur upwards) are expected to be able to transpose at sight from the key the composer wrote in (e.g. Trumpets in F for Tchaikovsky's 4th Symphony, Trumpets in E for parts of Dvorak's New World Symphony) to the key of their favoured instrument: usually B-flat in the UK, Southern Germany and Italy, C in the US, France and northern Germany...