Timbre is probably my favorite aspect of music. When I was younger, my idea of heaven was to be in a room with every orchestral instrument so I could play any one of them to enjoy their sound. Of course I love the timbres that can be produced on a cello but my favorite part of being in an orchestra is not playing in the cello section, it is listening to the other instruments!
Producing various timbres on a cello is mostly done with varying bow placement, speed and weight and varying the vibrato.
To me, the piano (which was the only instrument in our house when I was a child) had no timbre at all, but the beautiful instruments of the orchestra were each so different. It wasn't until I was 16 or so that I realized that the piano did have its own timbre. It's like when you realize that it's not just other people who speak with an accent and that perhaps your own speech is not the norm.
The type and/or brand of strings has a huge affect on the timbre of your cello.