dabei
there
Expresses that someone is present at an event or in a place.
Gestern war ein großes Fest in der Stadt, und ich war auch dabei.
Yesterday there was a big festival in the city, and I was there too.

there / with you
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there
Expresses that someone is present at an event or in a place.
Gestern war ein großes Fest in der Stadt, und ich war auch dabei.
Yesterday there was a big festival in the city, and I was there too.

'Dabei' is a pronominal adverb made up of 'da' and 'bei'. 'Da' refers to a thing or situation already known from the context. So it literally means 'bei dieser Sache' (with this thing) or 'an diesem Ort' (at this place).
Morgen ist ein wichtiges Meeting. Bist du auch dabei?
Tomorrow is an important meeting. Will you be there too?
The combination 'etwas dabeihaben' (to have something with you) means that you are carrying something with you. The object stands between the conjugated verb 'haben' (to have) and 'dabei'.
Ich habe meinen Ausweis nicht dabei.
I don't have my ID with me.
The expression 'dabei sein, etwas zu tun' (to be in the process of doing something) describes that you are right in the middle of an action. It is always formed with an infinitive construction with 'zu'.
Ich bin gerade dabei, das Abendessen vorzubereiten.
I'm in the middle of preparing dinner.
When 'dabei' connects two actions, it means that they take place at the same time. It refers to the action in the first part of the sentence.
Er telefoniert und macht sich dabei Notizen.
He is talking on the phone and taking notes while doing so.
In this meaning, 'dabei' introduces surprising or contrasting information. It can stand at the beginning of a sentence and then requires the verb to follow directly after it (inversion).
Er sagt, er hat keine Zeit. Dabei sitzt er nur vor dem Fernseher.
He says he has no time. Yet he's just sitting in front of the TV.
although
'obwohl' and 'dabei' can both express a contrast or something unexpected. However, 'obwohl' introduces a subordinate clause: the verb comes at the end. 'dabei' is more likely to appear in a main clause or to connect two statements more loosely. Learners may confuse the words because both show that one fact does not really fit well with another. If you want to form a clear subordinate clause with a counter-reason, use 'obwohl'. If you are adding a second, surprising piece of information, 'dabei' often sounds more natural.

Sie sagt, sie hat keine Zeit, dabei war sie den ganzen Nachmittag zu Hause.
She says she has no time, yet she was at home all afternoon.
Obwohl ich müde bin, lese ich noch ein Kapitel.
Although I am tired, I am reading one more chapter.