If you are not familiar with modules, check out Ansible - Getting Started with Modules.

The debug module can be used to print output.  In this example, "Hello World" will be printed.

- debug: 
    msg: "Hello World"

Or like this.

- debug: msg="Hello World"

When the play is run, the following should be produced.

TASK [debug]
ok: [server1.example.com] => {
    "msg": "Hello World"
}

name

Almost always, name is included to that some unique text in included in the output so that you know what debugging task is being executed.

- name: something unique
- debug: 
    msg: "Hello World"

Notice here that something unique is included instead of just the text debug.

TASK [something unique]
ok: [server1.example.com] => {
    "msg": "Hello World"
}

Using the var parameter

In this example, the vars plugin is used to create the foo variable.

vars:
  foo: "Hello World"

The debug module with the var parameter can be used to print the output of the foo variable.

- name: output the 'foo' variable
  debug: 
    var: foo

Or like this (notice the single quotes around foo).

- name: output the 'foo' variable
  debug: 
    var: 'foo'

Or like this (notice the double quotes around foo).

- name: output the 'foo' variable
  debug: 
    var: "foo"

When the play is run, the following should be produced, regardless if foo is unquoted, single quoted, or double quoted.

TASK [output the 'foo' var]
ok: [server1.example.com] => {
    "msg": "Hello World"
}

Often, debug is used along with the register module. In this example, the standard out, standard error, and return code of the ls (list) command will be stored in a variable named "out". 

- name: list command
  shell: "ls /tmp"
  register: out

You can then print the output using the debug module, like this.

- name: standard out
  debug: 
    var: out.stdout_lines

- name: standard error
  debug: 
    var: out.stderr

- name: return code
  debug: 
    var: out.rc

Using the msg parameter

The msg parameter is similar to the var parameter, except that the msg parameter can use Jinja2. Notice the double curley braces {{ ... }}. Jinja2 uses double curley braces for variables.

- name: output the 'foo' variable
  debug: 
    msg: "{{ foo }}"

When the play is run, the following should be produced.

TASK [output the 'foo' var]
ok: [server1.example.com] => {
    "msg": "Hello World"
}

Notice in this example that foo is wrapped in quotes. In Jinja2, when wrapped in quotes, foo is interpreted as a string. If foo were not wrapped in quotes, foo would be interpreted as a variable.

- name: output the 'foo' string
  debug:
    msg: "{{ 'foo' }}"

Which should produce the following.

TASK [output the 'foo' string]
ok: [server1.example.com] => {
    "msg": "foo"
}