Difference Between Mutable , Immutable string in C#

All .NET stings are immutable.
You cannot modify any string at all. All string operations create yet another string.
For example, if you have strings S1 and S2, S3 = S1 + S2 is a new string, while S1 and S2 remain the same.

In connection to that, imagine a loop adding to some string S (initially String.Empty) more and more portions at the end — a very typical task. As initial string S is never modified, actually, the the old value of S is concatenated with the new portion at the end and copied back to S. In this way, S is being assigned to a growing new string and all the data is copied every time.

In contrast System.Text.StringBuilder.Append does this thing much more effectively, because already available data is never copied again, the instance of StringBuilder mutates instead. If just two strings are added using "+" operations, it does not matter.
Same thing about comparison of string operations with StringBuilder operations.

As a rule of thumb, if you have any repeated operation to compose a string, always use StringBuilder. Basically, using more than one string "+" in one expression is not very effective; string.Format function is much better, faster and more readable.

—SA

A string instance is immutable. You cannot change it after it was created. Any operation that appears to change the string instead returns a new instance:

string foo = "Foo";
// returns a new string instance instead of changing the old one
string bar = foo.Replace('o', 'a');
string baz = foo + "bar"; // ditto here

Mutable and immutable are English words meaning "can change" and "cannot change" respectively. The meaning of the words is the same in the IT context; i.e.

a mutable string can be changed, and
an immutable string cannot be changed.

The meanings of these words are the same in C# / .NET as in other programming languages / environments, though (obviously) the names of the types may differ, as may other details.