In the new film on Yabla, La Tempesta, a conversation takes place down on the street. Paolo has had his car towed and doesn’t quite know how to get to work. His neighbor comments:
Nel senso, magari è la volta buona
I mean, maybe this will be the time
che ti fai una bicicletta pure tu.
that even you get yourself a bike.
Captions 4-5, La Tempesta - filmPlay Caption
Nel senso literally means “in the sense,” but Italians use it these days much as we use “I mean” in English. Lots of times they don’t even finish the sentence. Nel senso just stands alone, and you have to guess the rest. Nel senso can be likened to cioè (that is, meaning...), but technically, nel senso in this context should be followed by che (that) as in the following example.
Conoscendolo in che senso...?
Knowing him in what way...?
Nel senso che in paese le voci girano.
In the way that in town word gets around.
Captions 48-49, Il Commissario Manara - S1EP3 - Rapsodia in BluPlay Caption
Without che (or any other conjunction) following it, it's decidedly less grammatically correct.
Il senso is a noun that covers a lot of bases, but here, it is equivalent to "the way," "the manner."