What Does the Line '!/Bin/Sh -E' Do

What does the line #!/bin/sh mean in a UNIX shell script?

It's called a shebang, and tells the parent shell which interpreter should be used to execute the script.

#!/bin/sh <--------- bourne shell compatible script
#!/usr/bin/perl  <-- perl script
#!/usr/bin/php  <--- php script
#!/bin/false <------ do-nothing script, because false returns immediately anyways.

Most scripting languages tend to interpret a line starting with # as comment and will ignore the following !/usr/bin/whatever portion, which might otherwise cause a syntax error in the interpreted language.

Bash Script : what does #!/bin/bash mean?

That is called a shebang, it tells the shell what program to interpret the script with, when executed.

In your example, the script is to be interpreted and run by the bash shell.

Some other example shebangs are:

(From Wikipedia)

#!/bin/sh — Execute the file using sh, the Bourne shell, or a compatible shell
#!/bin/csh — Execute the file using csh, the C shell, or a compatible shell
#!/usr/bin/perl -T — Execute using Perl with the option for taint checks
#!/usr/bin/php — Execute the file using the PHP command line interpreter
#!/usr/bin/python -O — Execute using Python with optimizations to code
#!/usr/bin/ruby — Execute using Ruby

and a few additional ones I can think off the top of my head, such as:

#!/bin/ksh
#!/bin/awk
#!/bin/expect

In a script with the bash shebang, for example, you would write your code with bash syntax; whereas in a script with expect shebang, you would code it in expect syntax, and so on.

Response to updated portion:

It depends on what /bin/sh actually points to on your system. Often it is just a symlink to /bin/bash. Sometimes portable scripts are written with #!/bin/sh just to signify that it's a shell script, but it uses whichever shell is referred to by /bin/sh on that particular system (maybe it points to /bin/bash, /bin/ksh or /bin/zsh)

What does '#!/bin/sh -xe' mean?

I found this:

man sh:

-x xtrace        Write each command to standard error (preceded by
                            a ‘+ ’) before it is executed.  Useful for debug‐
                            ging.

-e errexit       If not interactive, exit immediately if any
                            untested command fails.  The exit status of a com‐
                            mand is considered to be explicitly tested if the
                            command is used to control an if, elif, while, or
                            until; or if the command is the left hand operand
                            of an “&&” or “||” operator.

It seems these are just error control options that make sure nothing worse happens if a command fails.

Why do you need to put #!/bin/bash at the beginning of a script file?

It's a convention so the *nix shell knows what kind of interpreter to run.

For example, older flavors of ATT defaulted to sh (the Bourne shell), while older versions of BSD defaulted to csh (the C shell).

Even today (where most systems run bash, the "Bourne Again Shell"), scripts can be in bash, python, perl, ruby, PHP, etc, etc. For example, you might see #!/bin/perl or #!/bin/perl5.

PS:
The exclamation mark (!) is affectionately called "bang". The shell comment symbol (#) is sometimes called "hash".

PPS:
Remember - under *nix, associating a suffix with a file type is merely a convention, not a "rule". An executable can be a binary program, any one of a million script types and other things as well. Hence the need for #!/bin/bash.

What is the preferred Bash shebang (#!)?

You should use #!/usr/bin/env bash for portability: different *nixes put bash in different places, and using /usr/bin/env is a workaround to run the first bash found on the PATH. And sh is not bash.