Next and the next
If we consider next as an adjective only, then typically it's used without a preceding the when referring to days of the week, or weeks, seasons, years and so on:
We're going camping next week.
My appointment is next Wednesday.
See you next year!
Otherwise, generally speaking, you would use the preceding the:
I'm speaking at the next board meeting.
Please bring in the next client.
Of course, these are generalisations, and there would be exceptions when speaking informally.