We divide hours into 60 minutes, and 60 minutes into 60 seconds because of the Babylonians. They had a base 60 number system where we have a base 10. Ie we don't typically questionn why the metric system is base 10, it just makes sense to us.

The 24 hour day comes from the Egyptians who originally divided the day into light hours, dark hours, and twilight hours. They had 10 light hours, 12 dark hours, and 2 twilight hours. That gives 24 hours. The (Egyptians had a base 10 number system like us but it was fairly different as they did not have place holders)

Indicating previous replies is not intended to discourage further questions. Please feel free to add follow-on questions, information, or debates.

The FAQ has several articles.

One is in "Language, Maps, Flags, And Time": "How were our current units of time agreed upon?", https://www.reddit.com/r/AskHistorians/comments/3vxb5d/how_were_our_current_units_of_time_agreed_upon/ , answered by /u/kookingpot .

Several are in "Calendars and timekeeping", but despite the section name, they're not really applicable:

• "What systems did civilizations use before they were introduced to the hour/minute/second idea? Are any such systems still in use?", https://www.reddit.com/r/AskHistorians/comments/1i1x4k/what_systems_did_civilizations_use_before_they/ -- but this is not directly applicable, because /u/jeanlucpeckinpah described the Chinese systems before modern hours and minutes, and [deleted] described the old Japanese system.
• "What event 00:00 (or 24:00) time points to and why?", http://www.reddit.com/r/AskHistorians/comments/1wjcuh/what_event_0000_or_2400_time_points_to_and_why/ -- but this has even less relevance, just talking about midnight and noon.
• "How were our current units of time agreed upon?", supra.