The comments on your question seem correct to me - that the word "ever" is used to enhance the meaning of "since".
There are some distinctions I would make:
Ever since that day, he has been like a different person.
This implies that something happened on that day that changed him, and he has been acting differently every day, consistently, between then and now.
Since that day, he has become a different person.
With "since", and no "ever", I can write a sentence that implies that he has changed somehow between then and now, but I don't say when. He could have changed three days after "that day", or it could have been yesterday. (This sentence also implies that the change happened because of some reason unrelated to "that day".)
Additionally, the word "ever" can be used to differentiate "since" from its other meaning, as a synonym for "because". Consider:
Since she started wearing purple, he has been wearing blue.
This could mean either that he started wearing blue because she started wearing purple, or that he started wearing blue after she started wearing purple, for reasons unconnected.
Ever since she started wearing purple, he has been wearing blue.
This sentence can only have the second meaning - that his wearing blue started after her wearing purple, but not necessarily as a result of it.