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

The set_fact module is used to create your own variable or array. In this example, the "foo" variable contains a value of "Hello World".

---
- hosts: all
  tasks:
    - set_fact: 
        foo: "Hello World"

AVOID TROUBLE

The -e or --extra-vars command line option or Extra Variables in Tower will take precedence over set_fact.

The debug module can be used to print the variable.

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

Which should produce the following.

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

Redefine variable

Let's say you used the vars plugin to give the "foo" key a value of "Hello", like this.

vars:
  foo: "Hello"

set_facts can be used to update the value of the "foo" key. In this example, the "foo" key will be updated to have a value of "World".

set_fact:
  foo: "World"

Array

Refer to Ansible - set_facts module (array of values) for the steps on how to create an array.

From an Ansible Fact to a variable

Commonly, set_fact is used to create a variable of an Ansible Fact. For example, let's say the df command on server1 returns the following.

[john.doe@server1 ~]# df
Filesystem                           1K-blocks     Used Available Use% Mounted on
/dev/sda1                               372607   170989    177862  50% /boot
/dev/sda2                               129774     6994    122780   6% /

Here is how you would create a variable named foo that contains the available bytes of /dev/sda1 (177862).

---
- hosts: localhost
  tasks:
  - set_fact:
      size: "{{ item.size_available }}"
    with_items: "{{ ansible_mounts }}"

  - debug:
      var: size
...

Which should return the following.

TASK [debug]
ok: [localhost] => {
    "size": "177862"
}

AVOID TROUBLE

Notice 177862 is wrapped in double quotes, meaning that the size variable contains a string, not an integer, which can be confirmed using the type_debug filter. This is because Jinja2 templating (the double curly braces) always returns a string. However, you can apply some of type filter, such as the bool or int filter in a when statement because Jinja2 templating cannot be used in a when statement.

---
- hosts: localhost
  tasks:
  - set_fact:
      size: "{{ item.size_available }}"
    with_items: "{{ ansible_mounts }}"

  - debug:
      msg: size is greater than 123456
    when: size | int > 123456
...

when

The when module can be used to set facts when a condition evaluates to true or false, like this.

---
- hosts: all
  tasks:
    - set_fact: 
        env: "dev"
      when: inventory_hostname is search ('dev')

    - set_fact: 
        env: "prod"
      when: inventory_hostname is search ('prod')