The Greeks visited Delphi so they could get advise from the god Apollo.
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Usually the ancient Greeks would visit an oracle in order to take decisions on major issues of the city states. Some of the most famous oracles were the Dodona oracle in Epirus, Delphi in the mainland, Delos the holy island of Apollo, Samothrace the island in the north part of the Aegean sea. Of course the oracle of Amun Ra of Egypt that even Alexander the Great visited before he conducted his second battle at Issus.
So they could get advice from the god Apollo.
Delphi
The ancient Greeks associated mountain exploration with bravery.
You are talking about the religion of the ancient Greeks; they were the deitites of ancient Greece.