After you have gained some mastery with a musical instrument, you can expect to become proficient on other instruments with much less effort. There are many reasons why this is good for developing your musical skills.
Many people start their instrumental education on the piano, but that instrument doesn't necessarily serve as a springboard to the orchestra or a marching band. A great second choice is the guitar. You can purchase a decent guitar nowadays without much expense. You can take it to parties and social events. There is a large repertory of music for guitar in many different styles. It is a great conduit for self-expression, and you may quickly find yourself motivated to write your own songs for enjoyment and as a way to meet new people.
Consider wind instruments, which bring their own advantages. They open up the worlds of symphonic performance, along with marching band, combos and ensembles, and even playing jazz. Flutes are melodic and engaging to play. And the breath control and good posture required to play a brass instrument can bring health benefits. The fun of playing any of these instruments with other musicians is something that must be experienced to fully appreciate.
There's also an entire world of percussion instruments to explore, and while virtuosity requires time and effort to achieve, the gratification that can be derived in the rhythmic realm is copious, and nowhere is it written that you must become a virtuoso on your second, or third, instrument. There are plenty of other benefits to—and reasons for—learning to play multiple instruments.
Having learned one instrument successfully, you already have the kinds of skills and discipline required to learn another. Probably the most important requirements for learning a musical instrument are some intelligence, willingness to stick with it, and the discipline to practice consistently. To some extent, your first instrument has already ingrained all of these in your character. The next instruments you learn will harvest some of the fruits of your previous efforts.
If you already play in a small band or orchestra, your ability to play an additional instrument makes you a more valuable group member. Your additional versatility allows you to fill in where you are needed. You may be just the player needed to add the voicing of your instrument to the group and give it a whole new dimension. If you're considering a career in music, you'll have many more possibilities in front of you as a multi-instrumentalist.
It's worth noting that you will be increasing your ability to read music when reading it for different instruments. If you enjoy writing music, knowledge of instruments notated in both the treble and bass clefs will make you a better composer and arranger. You'll be approaching your writing with additional perspective, bringing additional interest, variety, and possibilities to it.
As your knowledge of music and music making is broadened by your ability to play multiple instruments, you'll have more appreciation for the talents of others. You'll hear things in their music that you didn't hear before, and that can inform and enrich your own playing. At the very least you'll be expanding your repertoire of voicings, phrasing, styles, and songs.
If your primary instrument is not the piano, acquiring a music keyboard is advantageous to just about any musician. You'll find yourself using it for tuning, working out phrases, computer notation, and many other uses. With all the keys lined up sequentially, any musician can understand how it works and where to find the notes, making a keyboard an ideal second instrument.
At its most fundamental, learning additional instruments enhances your musicianship on all the instruments you play. What musician wouldn't want that?