This is an expression for talking about time loosely. "The next week or so" means "about the next week". It could be in 5 days, in 10 days, etc.

I'll be travelling for the next week or so.

Other phrases that use "or so" include:

• the first day or so
• the last year or so
• for an hour or so

For example:

This is one of the best songs I think I've heard in the last decade or so.