What to do next?

Looks like an old spike on a phalaenopsis (a photo of the plant itself can clear that up), in which case you can simply cut it off where it emerges from the plant,

 

That looks like a Phalaenopsis. The dried up flower spike can be clipped near the base, it's not contributing to the plant. Now you need to give the plant good care, it's next blooming will probably be in about a year. (A healthy Phalaenopsis can bloom again and again, for many years) If you can show some photos of the plant, you can get some good advice here on what you need to do to care for it. (Repotting, watering schedule, light) The ph

 

A beautiful, healthy plant. It probably needs repotting... the enemy of roots is soggy, airless, broken down medium. Your choice of medium is dictated by your watering practice... Sphagnum tends to stay wet, so you would water less often, the goal would be "gently damp", then water again. If you can water more often, you can use medium bark, which gives lots of air in the root zone but dries out much faster. Personally, I like to water, so I go for bark. Whichever medium you use the goal for the root zone is "humid air", not "wet", because too much wetness crowds out the air.