Recently one of my clients told me that "the twitter scene it is so daunting".
I remembered back when I first started and how I too just did not quite get it.
However I promise you Twitter actually has a pretty short learning curve to get started.
What is it that people are afraid of, I did some research and found 1) Fear of failure - "What if I do something wrong? Say the wrong thing?" This fear of Twitter can be overcome because of a short attention span, Twitter moves quickly and even if you were to "oh my gosh, make a mistake" it will not be visible for long.
Depending upon how many followers your followers your tweet could disappear in a second.
This quote is so very true, failure means you are actually doing something which is more than most people.

Every failure brings with it the seed of an equivalent success.
Napoleon Hill

2) New, too quick and big learning curve - even though Twitter may seem a little strange in the beginning think of it like being able to send a little brochure to millions of people.
The learning curve is not huge, there are only about 5 or 6 main features to learn.
Sitting down with someone for some focused learning and you could have it down pat in an hour.
3) Can be overwhelming - who do you follow, who not to follow or does it really matter? There are a lot of people who Tweet about "going to Starbucks for coffee" and may not care.
That's OK you just let that stream by, however it is a customer in your local area you may just decide that you need a coffee too and go and join them.
Twitter is used for Many, Many, Many reasons.
4) People believe they can't handle it - once you understand the power of Twitter you can effectively use it for your business in as little as 15 minutes a day.
You can use some of the many tools out there that make it much easier or you can have someone else assist you with your Tweeting.

Live as if you were to die tomorrow.
Learn as if you were to live forever.
Mahatma Gandhi

The real value of Twitter is listening.
You can easily see what your customers and potential clients are talking about, have concerns around or are looking for.
You may be able to quickly and easily "fill the gap" for them.