This is called a keiki. Some species, like equestris, throw keikis quite often, so depending on the ancestry this may be a common event.

Leave it on til it has several roots a few inches long, then you can remove it and pot it up (for giving). Or, if you like the look of the second plant on a spike, you can leave it on.

OK!
I'll just cut the bloom off and leave it lone for now. Then what wll happen as far as next year's flower stalk is concerned?
Thanks for responding,
Margie

if this is a phalaenopsis that does not throw keiki's it might not be a good sign. If they start growing Keikis it could mean the plant is dying and it is making babies to keep it's species alive. they do this when they don't like their enviroment. they do this in nature.
Of course I am saying this and right now I have a Phal. that had two spikes. After the flowers were gone i trimmed the spike to just above the 1st node. One spike is branching out and ready to produce flowers. like it is suppose to and the other spike is producing a Keiki. Some people leave their Keikis on and let them fall off by themselves. that's what happens to them in nature.