what is meant by connecting STDOUT and STDIN?

Standard input and standard output are not commands.

Imagine commands as machines in a factory with an assembly line. Most machines are designed to have one conveyor belt to feed data in and one conveyor belt to feed data out; they are the standard input and the standard output respectively. The standard error is an opening on the side of the machine where it can eject rejects.

+-------+     +------------------+       +------------------+     +------+
| input |     |    machine A     |       |    machine B     |     |output|
| reser ­­­|=====|<stdin     stdout>|=======|<stdin     stdout>|=====|bucket|
| ‑voir |  →  |      stderr      |   →   |      stderr      |  →  |      |
+-------+     +------------------+       +------------------+     +------+
                      ||                          ||

The diagram above shows a conveyor belt that goes through two machines. The data comes from the input reservoir on the left, is fed to machine A, then the output is conveyed further to machine B (for which it is input), and machine B's output is deposited in the output bucket on the right.

In unix terms, this is called a pipeline. The metaphor is that of plumbing: a pipe connects machine A to machine B. The shell syntax for the pipeline above is

<input-file.txt commandA | commandB >output-file.txt

The < redirection symbol tells the shell to connect commandA's standard input to the file input-file.txt before launching commandA. (You can put the redirection before or after the command name.) The > redirection symbol tells the shell to connect commandB's standard output to output-file.txt. The pipe ("|") symbol in the middle tells the shell to connect commandA's standard output to commandB's standard input before launching them.

Commands can have more than one input and more than one output, but that's material for another day.

standard input is a command that allows user to write to a file

Not a command, but a stream. Standard in and out are like mail boxes. When a program starts, it's given a box to recieve and a box to send mail. Usually, input comes from the keyboard and and is put in the in-box, mail put in the out-box ends up on your terminal screen.

standard output is a command that has the bash shell write output to the shell

The program doesn't actually know where standard out points. When you pipe A to B (as in $ A | B), when A puts mail in the out-box, it ends up in B's in-box. B processes the input and puts its own mail in the out-box, which is what you see on the terminal.

To drop the metaphore, as mentioned, standard in/out are streams. The mail box, or file descriptor, is one end of the stream. To pipe is to connect the standard out of A to the standard in of B.