There are many theories as to who they were. The wiki page has nine hypotheses.
What is the most widely accepted theory on who the ancient Sea Peoples were?
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The sea peoples are in Egyptian sources referred to as "foreign people of the sea". It is in other words a name they use for any sea-faring foreigners that attack Egypt. Some of the sources list the names of these sea peoples, making it clear that it is not one people that is meant.
The theories mentioned on Wikipedia may therefore all be correct at the same time.
The "sea peoples" that are mentioned by the Egyptians were probably, the Minoans....the ancient peoples of Crete. The Minoan Civilization lived and prospered during the Age of the Egyptian Pharaohs and Minoan Crete was also identified-(by the Greeks) as a "Thalassocracy"-(roughly translated as a "Sea Power" or "Rulers of the Sea"). Ancient Crete, (as well as present-day Crete), is located North of Egypt and trade (as well as diplomatic) relations between the 2 countries, was very likely. While there is no primary proof that the Minoans were the "sea peoples" referred to by the Egyptians, there is some interesting and intriguing circumstantial evidence.
The Egyptians may have also been referring to the Greco-Myceneans, who were also a seafaring peoples that settled into many Mediterranean territories once occupied by the Minoans-(including Crete proper). It is also plausible to suggest that the Greco-Mycenaeans may have had commercial and diplomatic relations with Pharaonic Egypt. The Myceneans, like the Minoan Cretans before them, also lived and prospered during the time of the Pharaohs. Again, while there is no primary proof supporting the Greco-Mycenean "sea people" thesis, a circumstantial case is not so implausible or unimaginable.
It is unlikely that the Egyptians were referring to the Carthaginians as "the sea peoples". While the Carthaginians did establish their own impressive commercial empire throughout much of the Mediterranean region, their civilization followed the centuries old Pharaonic Age and had thrived during the 1st millennium BC/BCE, though not beforehand.