Not to be confused with the capital city of the United Arab Emirates—that's written "Dubai" in German too, by the way—the German adverb dabei means generally "to be present" at some event, but can have many possible translations in English, depending upon the context. Let's take a look at some of the more commonly seen possibilities.
Ich freue mich, dass ihr heute dabei seid.
I'm happy that you are here today.
Caption 2, Eva erklärt: Sprichwörter
In this context, the use of dabei rather than simply hier implies "here with us."
Ich habe meine Lupe dabei, um die Schnecken zu sehen.
I have my magnifying glass with me to see the snails.
Caption 47, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen
You could possibly say bei mir in this context, although bei mir also means "at my place" or "at my house."
Warst du gestern bei der Schlacht dabei?
Were you present at the battle yesterday?
Caption 20, Bretten: Das Peter-und-Paul-Fest
Der Louvre ist nicht mit dabei.
The Louvre Museum is not participating.
Caption 8, Kunst weltweit: Galerienbesuch von zu Hause aus
The above two examples translate dabei as "to be present" at or "to be participating" in an event.
Wichtig ist dabei, immer Geld zu verdienen.
It is important to always make money thereby.
Caption 51: Fluglinien: Niki Air
The adverb dabei, when seen in its constituent parts da + bei, literally "there" + "by," forms the English adverb "thereby." Most people don't use the word "thereby" very often in everyday speech, however, and it's more common to use other equivalents.
Nun spring einfach hinab und flattere und schlackere dabei.
Now just jump down and flutter and flap as you do it.
Caption 26: Piggeldy und Frederick: Lernen fliegen
Another close equivalent to "thereby," and perhaps the most common translation in this context, is "in doing so":
Dabei passieren sie die fünf Kilometer lange Zeeland-Brücke.
In doing so, they pass through the five kilometer long Zeeland Bridge.
Caption 10, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen
The above could also have been translated: "They thereby pass through the five kilometer long Zeeland Bridge."
Go to Yabla German to find other examples of dabei used in a real-world context and see if you can find some other ways that it has been translated into English.