If you're a musician and anything like me, you can instantly recognize a Carlos Santana or Eric Clapton lick. Each of these musicians have their own sound, their own vibe. They have their own signature, which prompts the phrase "signature sound". Any good musician has to have one of these. Even if it's a way of playing their instrument, or a form of playing that they prefer.
To really find a signature sound, one would need to look towards someone with the most recognizable tone and style of all: Carlos Santana. If you don't know who this is, his most recognizable song would be "Smooth", released in his album "Supernatural". The song opens up with a fiery lick and transitions into a guajira/salsa type song, as most of Santana's style comes from. Although mainly latin rock, Santana plays across all genres of music, and still always achieves that signature sound.
In my time of playing guitar, I have always looked for my own signature sound. I imitated(to the best of my ability) the Carlos Santana sound and the Buddy Guy sound, creating a mix of chaotic, smooth, and passionate sounds. But as it turns out, imitating their sound only gets you so far. To truly form your own sound, you first need to know who you are, and be confident that you know. Second, you should have a visual in you mind of what exactly you want. What you want to sound like, what you want people to hear, and who your greatest inspirations are. For example, mine are Carlos Santana and Buddy Guy. Both have their distinct styles, so I emulate them and make it my own. I combine licks or mix the passionate slow playing of Santana with the quick, bluesy licks of Buddy Guy. Through this, I make my own signature sound.
Finding a signature doesn't only apply to music. It applies to writing, painting, and other art forms. For writing, a signature could mean a recognizable motif, and example being Robert Frost with his recognizable poems about nature. For art, a signature could be how the artist strokes the page with their brush, or a special flair at the end of the brushstroke. An obvious example would be Pablo Picasso, with his recognizable cubist paintings.
In all cases, finding a signature sound means finding yourself and projecting that through the art form. It means taking your heart and personality and displaying it through painting, music, etc.