Most Indians have this habit while speaking in English. It's not stammering that I'm aware of. It's not stuttering or bumbling either. I'm not sure what is it called.
The speech goes like this…
Hello everyone. I'm Maulik and here I am to present a….. our company's …..a……. balancesheet for the year of 2014-15. As we see, we are going through …a…….lots of ups and downs in a……
How is 'a' pronounced there? It's the same way we pronounce this indefinite article with any noun. So, it's 'a' in 'a car'.
It's not just with Indians, I have seen many foreigners (even natives) with this habit but the frequency is quite less.
The video: (Check at 00:56 and 1:01) – Note: Irfan's English is still better! The people I'm talking about have loud and clear 'a……a….a'.
https://www.youtube.com/watch?v=7oyGj8pFChM
Listen it carefully. There are several such pauses. I'm not sure whether the narrator is native – http://www.bbc.com/news/world-asia-27577537
Best Answer
Most non-Indians have the same habit! It's called a dysfluency because for a moment your speech stops flowing (fluent literally means "flowing freely"). And Codeswitcher's answer is correct; these are often referred to as filler.
Of course, we don't usually write this sound down, but when we do we usually spell it uh, not a. Even though it sounds like the indefinite article, we don't spell it like that because it's not being used as an article. Some speakers of non-rhotic dialects spell the same sound er—since they don't pronounce /r/ in this position, er and uh describe the same sound.
You can find it in a few dictionaries under uh. They typically list it as an exclamation or an interjection, and from time to time you'll find people saying uh on purpose to indicate that they're at a loss for words (even if they aren't really):
Bob is indicating that he can't think of anything nice to say. Poor Alice!