This is the 424th most frequent Russian word.
самые
"Самые" means "the most" or "the very" (superlative degree).
The word 'самые' is used here as a superlative adverb modifying 'высокие,' forming 'самые высокие' to mean 'the highest.'
Мы увидели самые высокие вершины в этих горах.
We saw the highest peaks in these mountains.
The word 'самом,' a variation of 'самые,' is used to emphasize 'центре,' indicating 'right in the most central part.'
Ты в самом центре города.
You are right in the very center of the city.
The word 'самые' is used here as a superlative adverb modifying 'интересные,' forming 'самые интересные' to mean 'the most interesting.'