Hello Adrian,
Suppose you are playing along with a clarinet player.
His is what is known as a b flat instrument; The keyboard is a c instrument.
So if you are both playing from the same music, perhaps in the key of C from the same sheet music, you will find that the clarinet , even though the player is playing a C it comes across as a B flat.
Not good; so you as a keyboard player can easily transpose your instrument downwards by two half steps.
That will make both instruments sound as if they are playing in the same key
Hope I have explained this clearly.
Another use for transpose is to change key during the song, perhaps as Toril said to not be too monotonous .
What I sometimes do is Kick it up a notch, as they say.
Example, you are playing a verse for a number of times followed by the chorus. The last chord is usually the closer. Let it play out for one measure, then play the 7th chord for one more measure while holding the transfer + button for one half step upwards......you will hear the difference right away... then repeat the chorus.
I hope this one is clear as well. takes a few trial runs to get the hang of it
Regards
Ron