The precise meaning is to act as a 'root' Expression to start a chain of Expressions inside a List context, i.e., inside arr.eval(....). I'll need to take a step back to explain...
'Root' Expressions
In general, only certain types of Expressions are allowed to start (or be the 'root' of) an Expression. These 'root' Expressions work with a particular context (select, filter,with_column, etc..) to identify what data is being addressed.
Some examples of root Expressions are polars.col, polars.apply, polars.map, polars.first, polars.last, polars.all, and polars.any. (There are others.)
Once we declare a "root" Expression, we can then chain other, more-generic Expressions to perform work. For example, polars.col("my_col").sum().over('other_col').alias('name').
The List context
A List context is slightly different from most contexts. In a List context, there is no ambiguity as to what data is being addressed. There is only a list of data. As such, polars.col and polars.first were chosen as "root" Expressions to use within a List context.
Normally, a polars.col root Expression contains information such as a string to denote a column name or a wildcard expression to denote multiple columns. However, this is not needed in a List context. There is only one option - the single list itself.
As such, any string provided to polars.col is ignored in a List context. For example, from the code from the Polars Guide, this code also works:
# Notice that I'm referring to columns that do not exist...
rank_pct = pl.col("foo").rank(reverse=True) / pl.col("bar").count()
Since any string provided to a polars.col Expression will be ignored in a List context, a single empty string "" is often supplied, just to prevent unnecessary clutter.
Edit: New polars.element expression
Polars now has a polars.element expression designed for use in list evaluation contexts. Using polars.element is now considered idiomatic for list contexts, as it avoids confusion associated with using col(“”).
