Commands inherit their standard input from the process that starts them. In your case, your script provides its standard input for each command that it runs. A simple example script:
#!/bin/bash
cat > foo.txt
Piping data into your shell script causes cat to read that data, since cat inherits its standard input from your script.
$ echo "Hello world" | myscript.sh
$ cat foo.txt
Hello world
The read command is provided by the shell for reading text from standard input into a shell variable if you don’t have another command to read or process your script’s standard input.
#!/bin/bash
read foo
echo "You entered '$foo'"
$ echo bob | myscript.sh
You entered 'bob'