In Genesis 10:25, there are 2 words which are notable to the question at hand. The passage reads
Two sons were born to Eber: One was named Peleg (פֶּ֗לֶג) because in his days the earth was divided, (נִפְלְגָ֣ה הָאָ֔רֶץ) and his brother’s name was Joktan.
According to pg 928 of the Hebrew and Aramaic Lexicon of the Old Testament (HALOT), the name פֶּ֗לֶג can mean division of tongues (like in Psalms 55:10) or an irrigation canal ("streams of water in a dry place" - like it is used in Isaiah 30:25, Psalms 46:5 and Psalms 65:10).
This word derives from פלג which means "to distance onself", "divide" or to "split" and it has a connotation of making a furrow. נִפְלְגָה ("to be separated") is also derived from פלג. Other word derivatives include פְּלַגָּה ("subdivision of a tribe") and פְּלֻגָּה ("division within a family"; as it is used in 2 Chronicles 35:5.)
Perphaps the most interesting relationship is to the town of Phalga (also called Saggaratum) located on the Euphrates where the Ḫabūr joins the Euphrates. According to the HALOT, the town name and פֶּ֗לֶג were syntactically related - a view shared by Emil G. H. Kraeling of Columbia University. This town is near the Ziggurat of Mari and Saggaratum was the capitol of the kingdom of Zimri-lim who's rule was from 1775 to 1761 BC when he was conquered by Hammaurabi. This works out very nicely if you are of the opinion that the Tower of Babel was a Ziggurat and the dates would be consistent with an 18th Dynasty exodus from Egypt.
Furthermore, radiometric dating of archaeological and paleontological evidence indicates that while Pangaea did exist at one point, it was several million years before Neolithic and Calcolithic eras and occured in three phases spanning several million years which would also be inconsistent with a rapid event occuring over the lifetime of one man (peleg).
The radiometric dating methods used for dating the fossil evidence of Pangea and the continental drift are extremely accurate. While it would be possible for one dating method to be skewed by a sudden influx of a given element into the atmosphere (Potassium, in the case of Potassium-argon dating for example), it would be highly unlikely for this situation to occur for multiple unrelated elements. Accordingly, since the many dating methods are able to corroborate each other we can rest assured that these methods are accurate. The logarithmic decay curves are also known to be accurate since radioactive isotopes degrade at a known and observed constant rates and the observed laws of physics would have to have differed over time or simply be wrong for these dating methods to be inaccurate.
Accordingly, while the linguistic evidence may be ambiguous, the historic context and scientific evidence are not and the simplest explanation is that this should be regarded as the division of people groups and language.