On time means that there is a specific time established when something is supposed/expected to happen, and it is happening at the planned time.
If you say "He's always on time" it means he is punctual; he always arrives at the correct time, he is not late.
If you say "He's never on time" it means he is always late.
In time means that something happened at the last moment before it was too late; before something bad would happen.
- The accident victim was seriously injured; they got him to the hospital just in time.
(If they hadn't arrived at the hospital, he might have died)
- I missed the opportunity to go to that college because I didn't submit my application in time.
- I left home early and arrived in plenty of time to catch my flight.
- I got stuck in traffic and arrived just in time to catch my flight.