A friend of yours is throwing a party (notice that we say throwing a party; we can also say organising or giving, but not making). You want to assure him of your presence, so you say ... ?
Well, in Polish, we might say: Będę. But in English, we can't just say, I'll be. To an English speaker, I'll be means I will exist. In this situation, we want to say: I'll be there. In fact, "I'll Be There" was the name of a big Jackson Five hit back in 1970. The word there doesn't have to refer to a specific physical location:
I'll always be there for you. (Where? Wherever you are.)
Normally, in fact, it makes no sense to say I'll be. However, in some cases people do say it, usually stressing both syllables. It's a short way of saying:
I'll be damned
I'll be dipped
I'll be a monkey's uncle, etc.
all of which are ways of expressing extreme surprise--to show that something has happened that you certainly didn't expect to happen.
You say SUSAN is a doctor now? The same Susan I used to know? Well ... I'll be.