The literal answer is as others have given: because the current directory isn't in your $PATH.

But why? In short, it's for security. If you're looking in someone else's home directory (or /tmp), and type just gcc or ls, you want to know you're running the real one, not a malicious version your prankster friend has written which erases all your files. Another example would be test or [, which might override those commands in shell scripts, if your shell doesn't have those as built-ins.

Having . as the last entry in your path is a bit safer, but there are other attacks which make use of that. An easy one is to exploit common typos, like sl or ls-l. Or, find a common command that happens to be not installed on this system — vim, for example, since sysadmins are of above-average likelyhood to type that.

Does this sound too theoretical? It largely is, but it definitely can happen in reality, especially on multi-user systems. In fact, here is an example from this site where an administrator switched to a users' home directory and found ps to be masked by an executable of that name.

try:

abc/info.exe

but if it's really a Windows program, you will need to install "wine", then do:

wine abc/info.exe

but only some Windows programs will work under wine.

Your script should look like:

#!/bin/bash

passwd

Save it in a file, let say password.sh or simple password, then make it executable using next commands in terminal:

cd /path/to/password.sh  #or cd /path/to/password
chmod +x password.sh     #or chmod +x password

To run it from terminal, just use the following command:

./password.sh            #or ./password

or

/path/to/password.sh     #or /path/to/password

To run it only using:

password.sh              #or password

you must to add the path of the script to the PATH. See How to add a directory to the PATH? in this sense.

The definitive answer to "how programs get run" on Linux is the pair of articles on LWN.net titled, surprisingly enough, How programs get run and How programs get run: ELF binaries. The first article addresses scripts briefly. (Strictly speaking the definitive answer is in the source code, but these articles are easier to read and provide links to the source code.)

A little experimentation show that you pretty much got it right, and that the execution of a file containing a simple list of commands, without a shebang, needs to be handled by the shell. The execve(2) manpage contains source code for a test program, execve; we'll use that to see what happens without a shell. First, write a testscript, testscr1, containing

#!/bin/sh

pstree

and another one, testscr2, containing only

pstree

Make them both executable, and verify that they both run from a shell:

chmod u+x testscr[12]
./testscr1 | less
./testscr2 | less

Now try again, using execve (assuming you built it in the current directory):

./execve ./testscr1
./execve ./testscr2

testscr1 still runs, but testscr2 produces

execve: Exec format error

This shows that the shell handles testscr2 differently. It doesn't process the script itself though, it still uses /bin/sh to do that; this can be verified by piping testscr2 to less:

./testscr2 | less -ppstree

On my system, I get

    |-gnome-terminal--+-4*[zsh]
    |                 |-zsh-+-less
    |                 |     `-sh---pstree

As you can see, there's the shell I was using, zsh, which started less, and a second shell, plain sh (dash on my system), to run the script, which ran pstree. In zsh this is handled by zexecve in Src/exec.c: the shell uses execve(2) to try to run the command, and if that fails, it reads the file to see if it has a shebang, processing it accordingly (which the kernel will also have done), and if that fails it tries to run the file with sh, as long as it didn't read any zero byte from the file:

        for (t0 = 0; t0 != ct; t0++)
            if (!execvebuf[t0])
                break;
        if (t0 == ct) {
            argv[-1] = "sh";
            winch_unblock();
            execve("/bin/sh", argv - 1, newenvp);
        }

bash has the same behaviour, implemented in execute_cmd.c with a helpful comment (as pointed out by taliezin):

Execute a simple command that is hopefully defined in a disk file somewhere.

1. fork ()
2. connect pipes
3. look up the command
4. do redirections
5. execve ()
6. If the execve failed, see if the file has executable mode set. If so, and it isn't a directory, then execute its contents as a shell script.

POSIX defines a set of functions, known as the exec(3) functions, which wrap execve(2) and provide this functionality too; see muru's answer for details. On Linux at least these functions are implemented by the C library, not by the kernel.