When people refer to a character as being safe, it generally means that they have a good number of moves that are safe on block. Likewise, a character who doesn't have many is called unsafe. If you want to see what moves are safe or unsafe on block, what you want to do is go into training, pause, set "move details" to left (or right, if your hp bar is on the right side of the screen), and set the training dummy to block all attacks.
First, I'll give a drastic oversimplification. Look at number labelled 'advantage' in the top right of the details box. Have the dummy block any move. If that number is -7 or less, the move is unsafe. If it is -4 or more, it's safe.
In more detail, though, that number shows the difference in recovery for both characters, the bigger the number, the bigger the difference, and is generally categorized with three labels: Advantage, neutral, and disadvantage. Disadvantage also has three further subcategories: Safe, semi-safe and unsafe.
In DoA, the most effective way to punish a blocked move is usually to throw, so that's the measure by which a move is judged safe or unsafe. If a move is unsafe, that means that after blocking the move, your opponent can use a command throw on you, and there's no way you can prevent it. Command throws are unbreakable, and you don't leave recovery fast enough to avoid it or retaliate. Since most characters have a command throw with a 7 frame start up, this means that any move that leaves you at -8 or less can be punished this way. Some characters, like Tina, have a 6 frame command throw, so this number changes to -7.
If a move is semi-safe, it means that the only way they can punish it is with a neutral throw. Neutral throws are faster than command throws, but they can be broken, so you're not guaranteed to take damage from it. Most characters have a 5 frame neutral throw, so a move that is -6 or -7 can only be punished this way. Again, some characters such as Tina have 4 frame neutral throws, so this becomes -5 or -6 against them.
If a move is safe, it means that, while it still leaves you at disadvantage, your opponent has no means of punishing you for it. If they try to throw you, you can crouch, or even strike, thwarting any punishment attempts. However, you are still at disadvantage, so if you both tried to use a quick strike after it, they will still hit you first. A move that is safe is -1 to -5 for most characters, and -1 to -4 for special cases.
Hope this helped. I can try to explain a bit better if there's something you don't get.
