Name for a "lookup" table with values in separate rows
Removing repeating groups (your comma delimited values) and moving this data into another table where each value is a row in that table is called normalization.  In particular, you're moving from 0 Normal Form (0NF) to a higher normal form, (1NF or higher, depending on what functional dependencies remain).  

In your specific example, once you split out the favourite foods into a child table you might be in either 1NF or 3NF, depending on whether you also have a "master table" of food types.

The new child table where the favourite foods are recorded might be considered an intersection table, particularly if you also have a master table of all of the foods listed one record per type of food.  This is the typical way in which a many-to-many relationship is implemented in a relational database.

If you have this master table of food types, you would be in 3NF.  If you don't your child table might not be considered to be 3NF, just 1NF, because the list of foods is subject to update anomalies and possibly delete anomalies - depending on how your system views foods themselves, independent of their relationship to people.