unterwegs
on the way
On the way to a destination; currently between the starting point and the destination.
Ich rufe dich später zurück, ich bin gerade unterwegs.
I'll call you back later; I'm on the way right now.

on the way / out and about
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on the way
On the way to a destination; currently between the starting point and the destination.
Ich rufe dich später zurück, ich bin gerade unterwegs.
I'll call you back later; I'm on the way right now.

'Unterwegs' is made up of the preposition 'unter' (under / among) and 'Wegs', an old genitive form of 'Weg' (way). So it literally means something like 'of the way' or 'on the way'.
Ich kaufe das Brot, es liegt direkt auf dem Weg.
I'll buy the bread; it's right on the way.
The adverb 'unterwegs' is almost always used with a form of the verb 'sein' (to be). The typical construction is: 'jemand ist unterwegs' (someone is on the way / out and about).
Wann kommst du? Ich bin schon unterwegs.
When are you coming? I'm already on the way.
The exact meaning depends on the context. Words like 'gerade' (right now) or 'jetzt' (now) emphasize that someone is on a specific route. Adverbs like 'viel' (a lot), 'oft' (often), or the addition 'beruflich' (for work) tend to describe a traveling lifestyle.
Ich kann gerade nicht telefonieren, ich bin unterwegs zum Bahnhof.
I can't talk on the phone right now; I'm on the way to the train station.
outside / outdoors
'unterwegs' and 'draußen' can both mean that someone is not at home or not in the room. The most important difference is: 'unterwegs' emphasizes the route, movement, or the fact that someone is currently away from home. 'draußen' emphasizes the place outside a building or outdoors in nature. So you can be 'draußen' without being 'unterwegs', for example in the garden. And you can be 'unterwegs' even if you are sitting on a train or in a car. Learners often confuse the words because both have to do with 'not inside'.

Lea ist gerade unterwegs zur Arbeit und kann nicht ans Telefon gehen.
Lea is on her way to work right now and cannot answer the phone.
Karim sitzt draußen im Garten und liest für die Prüfung.
Karim is sitting outside in the garden and studying for the exam.