Looks like a Den. nobile hybrid. They like. Lots of light, water and fertilizer when they're in active growth, and a cool dry rest when the canes are fully formed. Search for "Den. nobile care" or "Yamamoto Dendrobium care" and you'll get good info.
it looks like you have some keikis going on some of the canes...keikis are baby plants, that grow off portions of the main plant....that is where your roots are coming from....you can gently pry the keiki off the main stem where it attaches, just a little twist is normally enuf to dislodge it....and pot it up separately from the mother....be sure to label it and date the label....
Nobile type Dens. need some specialized care in order to bloom each year. Yours is a Yamamoto hybrid, and I would read through his website for details on the care, as it is a bit different than the care of Den. nobile the species. I grow several of these and they are very rewarding plants.