When you use the + operator to build up a string:
string s = "01";
s += "02";
s += "03";
s += "04";
then on the first concatenation we make a new string of length four and copy "01" and "02" into it -- four characters are copied. On the second concatenation we make a new string of length six and copy "0102" and "03" into it -- six characters are copied. On the third concat, we make a string of length eight and copy "010203" and "04" into it -- eight characters are copied. So far a total of 4 + 6 + 8 = 18 characters have been copied for this eight-character string. Keep going.
...
s += "99";
On the 98th concat we make a string of length 198 and copy "010203...98" and "99" into it. That gives us a total of 4 + 6 + 8 + ... + 198 = a lot, in order to make this 198 character string.
A string builder doesn't do all that copying. Rather, it maintains a mutable array that is hoped to be larger than the final string, and stuffs new things into the array as necessary.
What happens when the guess is wrong and the array gets full? There are two strategies. In the previous version of the framework, the string builder reallocated and copied the array when it got full, and doubled its size. In the new implementation, the string builder maintains a linked list of relatively small arrays, and appends a new array onto the end of the list when the old one gets full.
Also, as you have conjectured, the string builder can do tricks with "unsafe" code to improve its performance. For example, the code which writes the new data into the array can already have checked that the array write is going to be within bounds. By turning off the safety system it can avoid the per-write check that the jitter might otherwise insert to verify that every write to the array is safe. The string builder does a number of these sorts of tricks to do things like ensuring that buffers are reused rather than reallocated, ensuring that unnecessary safety checks are avoided, and so on. I recommend against these sorts of shenanigans unless you are really good at writing unsafe code correctly, and really do need to eke out every last bit of performance.
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