It refers to the southern part (mediodía) of the Iberian Peninsula. You could say that, or "southern Iberia", but this evidently refers to Ancient Rome, when this region was the province of Hispania, so I think "southern Hispania" would be suitable; this name is commonly projected back, as it were, to the pre-Roman era. I don't think "southern Spain" would be suitable here, since it refers to both Spain and Portugal, and Spain did not exist as such then.

"Tartessos significó la puesta en marcha de una estructura urbana a partir del mediodía hispano desde una etapa precolonial"
https://books.google.co.uk/books?id=uQmdTzQ-tlkC&pg=PA21&lpg...

"This process started with the Roman acquisition of the former Carthaginian territories in southern Hispania and along the east coast as a result of defeating the Carthaginians (206 BC) during the Second Punic War (218–201 BC), leading to them leaving the peninsula."
https://en.wikipedia.org/wiki/Roman_conquest_of_the_Iberian_...

"The foundation of the Caesarian and Augustan colonies marks the birth of the Roman urban system in eastern and southern Hispania. [...]

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Note added at 32 mins (2019-03-11 10:31:50 GMT)
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URL for the last reference: https://www.thebritishacademy.ac.uk/pubs/proc/files/86p291.p...