Fabian Pascal recently blogged on the definition of first normal form. Also, his Practical Database Foundation Series includes a treatment of normalization and 1NF. If one purchases the entire series two additional papers are included that specifically address what is and what is not 1NF, the former paper written by CJ Date. I will make an attempt to summarize the key points with regard to your question.
For a table to be in 1NF, and thus be a relational table (R-table), certain rules must be followed in its design and population to ensure the table can acquire the properties of a mathematical relation. The rules summarized are:
- Distinct un-ordered rows
- Uniquely named un-ordered columns
- Single Value Columns (SVCs)
- No missing column values
Regarding rule one, a mathematical relation by definition has unique tuples but when adapted for use in data management Codd added a key to serve as a unique identifier for each row as in the real world entity types are identified by one or more of their characteristics (attributes). Note there can by more than one candidate key so I just use the word key here.
Regarding rule four, Codd initially intended that no column could contain a relational valued domain (RVD). It was later shown that RVDs do not violate the relational model and instead any domain of any complexity, including another relational variable, could be contained in the column of an R-Table so long as that column contained only one value.
The table you have shown in the question and labeled as UNF format is not in 1NF as it violates a portion of the first rule - distinct rows - if I interpret the diagram correctly that Customer Number is the key based on the single underline under its name. There are three rows with customer number C002.
Of the two tables shown which you believe to be in 1NF, the first is still not in 1NF as it still contains three rows with the same customer number C002. The second table is in 1NF as it has unique rows as defined by the key of customer number and item reference. Note that the original table does not require splitting to achieve normalization. Instead, the original table could be changed to have as its key customer number plus item reference and it would be in 1NF.