A normal throw is a throw with a command common to all characters in a game (usually). Throws that do not fit this description are known as command throws. They are typically easy to perform in principle, but the effectiveness and properties vary widely from game to game. Most games have them.
In some games, such as in the King of Fighters series, where there is no miss animation for these (instead coming out as an misfired normal or command move owing to the simple execution: hit forward and backward plus an appropriate button at the same time), normal throw attempts do not leave you open, which makes them useful.
The other school of normal throws involves simultaneous pressing of buttons (such as SFIII: 3rd Strike). This makes their use more exacting; they will generally have a miss animation, which penalizes a failed attempt.
However, depending on the particular game, there will be things like throw escapes, and normal throws may take more than one frame to perform, so they are not necessarily surefire performers so much as a part of your tactics.
In many games, a single character will have roughly two (maybe more, occasionally less) kinds of normal throws. They are generally distinguished by the difference in their invocation method (punch vs. kick, forward vs. neutral vs. back, etc.).