Hi Mimi,
Yes, its a cymbidium. When my Mum first gave it to me it had 4 spikes. I keep it in the conservatory in the winter and then put it outside once chance of frosts have gone. The first year I watered it lovingly outside (rain, not tapwater), then fed it in the Autumn. It did nothing - not even 1 bud.
So last summer I just stuck it outside behind the garage and just chucked a bucket of rain water over it now and again (i.e. when I remembered). I started to feed it with orchid food when i brought it in again, and its rewarded me with this lovely display.
In the winter, or dry weather, I revert to tap water, but let it stand for a day or so before using it. Don't know if this makes a difference or not. It's also very very pot bound, whch they love apparently - they like it cosy, not spacious!!
Good luck with yours Mimi