There are two concepts and ideas that happen in music which, when combined, explain why this happens.
The first is that the way certain instruments are constructed affects what sounds they can produce. The E♭ alto saxophone, the B♭ clarinet, and the horn in F each can easily play in the key designated. Typically, when learning to play these instruments the scales and pieces you would play would be in the key of the instrument. Those instruments can be constructed in other keys and sometimes are, but the popular key that they are built in tends to best take advantage of the timbre and the range of that instrument.
The second is that we tend to center the basics of what an instrument can play around C. So combined with the fact that instruments are built with one key being easier to play in than the others, it's common to call the easiest key to play in "C" even though it may not actually be C.
This may seem confusing, but there is one big advantage to doing this which is that someone who can play an instrument in a transposing family like the saxophone can keep the fingering the same in the notation. Wikipedia sums it up nicely:
The instruments in these families have differing ranges, with the
members sounding lower as they get larger; but an identical pattern of
fingerings on two instruments in the same family produces pitches a
fixed interval apart. For example, the fingerings which produce the
notes of a C major scale on a standard flute, a non-transposing
instrument, produce a G major scale on an alto flute. As a result,
these instruments' parts are notated so that the written notes are
fingered the same way on each instrument, making it easier for a
single instrumentalist to play several instruments in the same family.