I am working with spark and scala and saw the following in the online docs
df.select($"name", $"age" + 1).show()
What does $"name" mean here?
This is not a scala thing.
scala> val name = "something"
name: String = something
scala> println($"name")
<console>:12: error: value $ is not a member of StringContext
       println($"name")
               ^
Rather a spark thing, which seems to represent a column.
See the org.apache.spark.sql.SQLImplicits code over here,
  implicit class StringToColumn(val sc: StringContext) {
    def $(args: Any*): ColumnName = {
      new ColumnName(sc.s(args: _*))
    }
  }
You could simply do dataframe.select("columnname").show or dataframe.select(col("columnname")).show too, but dataframe.select($"columnname") to mutate the column value, like you are incrementing age in your example. 
eg.
Given a dataframe,
 +----+-------+
 | age|   name|
 +----+-------+
 |null|Michael|
 |  30|   Andy|
 |  19| Justin|
 +----+-------+
scala> dataframe.select($"name".as('myname)).show()
+-------+
| myname|
+-------+
|Michael|
|   Andy|
| Justin|
+-------+
scala> dataframe.select("age"+1).show()
org.apache.spark.sql.AnalysisException: cannot resolve '`age1`' given input columns: [age, name];;
'Project ['age1]
Other example to use $ could be filter based on column values, 
dataframe.filter($"age" > 28).show()
So, basically, you are making it a variable(of type Column) with $"" in Spark.
Scala has ${} while concatenating the variables, (aka String interpolation)
scala> val printMe = "prayagupd"
printMe: String = prayagupd
scala> println(s"value = $printMe")
value = prayagupd
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