The word "time" has different meanings.  Sometimes it is an uncountable noun meaning the perceived continuum of the past, present, and future, as regarded as a whole.   This is your время.

But the word "time" can also mean a specific period or portion of the continuum.  These periods and portions sometimes are often expressed in Russian as "раз", and are countable.   Examples:  I have been to France two times (два раза)...    This is the first time (первый раз) I have ever listened to the music of Tchaikovsky.  ---  Other times you would express the idea of a period or portion of time with the Russian word время, not раз, but in English we would still use the word "time":   I had a great time at the party. (Я прекрасно провёл время ...).