Thank you both for your replies!

And right, racemes it is!
I've had this orchid for maybe 10 years, and it was not tiny when I got it, so I'm not sure if it has to do with it maturing, but maybe orchids take a very long time to mature (like humans?) :P It sure is quite a monster today.
The only difference that I've done now and never before is that I pollinated two of its flowers, one of them showing in the picture. Another new thing for this orchid is that it has its first keiki (basal), never had that before on this one. I'm not sure why it's suddenly thriving, if that is what it is.