Learn Hardcore Arabic (Egyptian): عندنا اجتماع مع المدير الساعة سبعة الصبح. - We have a meeting with the manager at seven in the morning.

ج in Egypt is usually pronounced like g in go, so اجتماع sounds like egtimāʿ.
الساعة is usually pronounced es-sāʿa.
الصبح is usually pronounced with an emphatic s, roughly ṣ-ṣobḥ.

What does عندنا mean exactly?

عندنا literally means at us, but in everyday Arabic it usually means we have.

It breaks down like this:

So عندنا اجتماع literally means something like at us, there is a meeting, which English expresses as we have a meeting.

Why is there no separate word for have in this sentence?

Because Egyptian Arabic usually does not use a verb like English have in this kind of sentence.

Instead, possession is often expressed with عند:

So:

This is a very common Arabic pattern.