It is very important to save money, as that gives you the opportunity to have some money in bulk to start up a business or a given project. Saving money from your monthly or weekly income is very important.
Most persons become poor because they spend all the money they receive as salary and neglect savings. But just like the OP have rightly said, is saving enough? No. Because your need to invest your savings to bring in more money for you and in that your savings increase.
I disagree with that statement. Saving is not a solution to evade to become poor. You know, there are people who live poor, but still manage to save something. When someone save, lets say 5% of his salary, poor people save 0.1% only. Those who spend all salary and become poor either have low earnings or are bad at managing finances. Some people even manage to spend during month more than they have received as a salary this month, and they dont look poor at all.