In italian, segno means sign, and in music theory its symbol is:
Italian, Dal segno (D.S.) means from the sign, and in music theory it is like a repeat sign: You had to repeat the section between two signs, like this:
We play the first measure, and you can notice the two symbols 
We play the second measure and we notice that there is a repeat sign
We play the third measure which ends with another repeat sign
After playing the third measure, we go back to the first repeat sign
We play the second measure one more time.
We play the third measure one more time.
We go our way quietly.
The second sign can be replace by D.S or by Dal Segno, but it is the same:
We play the first measure, and you can notice the symbol
We play the second measure and we notice that there is a repeat sign
We play the third measure which ends with the letters D.S. which means Dal Segno (go to the sign in Italian).
So after playing the third measure, we go back to the first repeat sign
We play the second measure one more time.
We play the third measure one more time.
We go our way quietly.
Dal segno al fine
In italian, Dal segno al fine means from the sign to end, so after you go back to the sign you have to stop at the Fine indication, like this:
We play the first measure, and you can notice the symbol
We play the second measure.
We play the third measure and you notice the symbol
We play the fourth measure.
We play the fifth measure, and you notice the Italian word Fine (end in Italian) at the end of this measure.
We play the sixth measure.
The seventh measure has a final double bar, but this is not the end of the piece because you will notice that there is D.S. al Fine (Dal segno al Fine) which in Italian means go to the sign then to the end.
So we go to the sign
We play the third measure one more time.
We play the fouth measure one more time.
We play the fifth measure one more time.
And we stop here because of the Italian word Fine (end in Italian).
Ancient notation of Dal Segno
In some ancient music score, you will find this:
But it is the same, the sign was different.
