What is meant by register?

“A great many people are a little confused about register. They slip from grotesque compound abstractions into a slangy tongue that jars a great deal. This is the aesthetic part of writing but it is still a significant part. Aesthetics are not simply the icing on the cake. What matters is how you present material convincingly without problems that detract from the message. I see the register and the aesthetics as more of a problem in academic writing than grammar. Style adds to the communication process. Keep an eye on abstractions.”