What does the <> operator do in Slick?

It's not a scala operator, it's a method defined by slick's ShapedValue class

As you can see in the documentation you linked, it's used to map a projection to and from a case class providing two methods

 def * = (id.?, first, last) <> (User.tupled, User.unapply)

The <> operator defines a relation between a Row in the Table and a case class.

case class User(id: Option[Int], first: String, last: String)

ROW            |id             | first        | last        |

So the data first is taken out of the Tabels as an n-tuple (left side of <>) and then transformed to the case class (right side of <>).

To make the transformation of the case class work one needs two kinds of methods:

Row to n-tuple to case class.

scala> User.tupled
res6: ((Option[Int], String, String)) => User = <function1>

So this function can create a User when given a triple (Option[Int], String, String) as an argument.

case class to n-tuple to be written in DB.

scala> User.unapply _
res7: User => Option[(Option[Int], String, String)] = <function1>

This function provides the functionality with the other way round. Given a user it can extract a triple. This pattern is called an Extractor. Here you can learn more about this: http://www.scala-lang.org/old/node/112

If you clone the Slick source repo and grep for def <>, you'll find that <> is a method of ShapedValue that returns a MappedProjection.