In a recent episode of Stai lontana da me, some form of the word impegno or impegnarsi appears three times in a row, each time with different connotations. Let's have a look.
The noun form impegno can refer to a commitment at work, an errand, an appointment.
Comunque abbiamo un sacco di cose in comune,
Anyway, we have a lot of things in common,
gli impegni di lavoro, l'intimo.
work obligations, underwear.
Captions 22-23, Stai lontana da me - Rai CinemaPlay Caption
It's a convenient way to be vague:
Ho un impegno (I have a [prior] commitment).
We can use the adjective form impegnato to mean "busy":
Sono impegnato al momento (I'm busy just now).
The reflexive verb form impegnarsi means "to commit" or "to make a commitment." In the video, the two people are talking about a commitment in matters of the heart:
Il terrore di impegnarsi.
The terror of commitment.
Caption 24, Stai lontana da me - Rai CinemaPlay Caption
But it can also mean "to try very hard," "to make an effort":
Mi sto impegnando molto ma i risultati sono scarsi.
I'm really trying hard, but the results are poor.
The expression senza impegno (literally "with no obligation") sometimes means, "don't feel you have to." It can also make it clear that we're talking about something very casual, which may be the case in the breakfast invitation below.
Colazione insieme? Senza impegno, eh.
Breakfast together? No obligation, huh.
Captions 25-26, Stai lontana da me - Rai CinemaPlay Caption
In more commercial settings senza impegno can mean "you don't have to sign anything and there's no charge."