How to correctly pass argument to final 'if' conditional when column formatting using JSON?

The if expression requires 3 arguments:

• Condition
• TRUE result
• FALSE result

When you are nesting if expressions you are providing the nested if expression as the FALSE result. Generally, the final FALSE result is the default result (when nothing else matches use this). So, with your nested conditions the last if is unnecessary and can just be replaced with the default value.

{
    "$schema": "https://developer.microsoft.com/json-schemas/sp/v2/column-formatting.schema.json",
    "elmType": "div",
    "children":
    [
        {
            "elmType": "span",
            "style":
            {
                "display": "inline-block",
                "padding": "0 10px 0 0"
            },
            "attributes":
            {
                "iconName": "=if(@currentField == 'Value 01', 'TextDocument', if(@currentField == 'Value 02', 'FileImage', if(@currentField == 'Value 03', 'MSNVideos', 'Website')))"
            }
        },
        {
            "elmType": "span",
            "txtContent": "@currentField"
        }
    ]
}

Expressions are written on a single line which makes them hard to follow when you've got anything but a simple expression. The iconName expression is easier to understand if broken across lines:

=if(@currentField == 'Value 01',
    'TextDocument',
    if(@currentField == 'Value 02',
        'FileImage',
        if(@currentField == 'Value 03',
            'MSNVideos',
            'Website'
        )
    )
)

As you can see above every if expression has 3 arguments. Hope that helps!