If your university has enabled Web Services for the mobile app, you can generate your own API token and call the Web Services used by the mobile app. If the latter are not enabled, you have to get in touch with your administrator to get Web Services access.
Demo using moodle.org
First, let's get an API token (replace $USERNAME with your username, and $PASSWORD with your password):
$ curl -d username="$USERNAME" -d password="$PASSWORD" 'https://moodle.org/login/token.php?service=moodle_mobile_app'
{
  "token":"SNIPTOKEN",
  "privatetoken":"SNIPPRIVATE"
}
Next, we need your userid, it will be used throughout other web services call. You can obtain your userid by calling the web service core_webservice_get_site_info. Make sure to replace $TOKEN with the token you obtained above.
$ curl -d wstoken="$TOKEN" -d wsfunction=core_webservice_get_site_info 'https://moodle.org/webservice/rest/server.php?moodlewsrestformat=json' | python -m json.tool | grep userid
"userid": 1451616,
Now that you have your userid, we can request the courses that you are enrolled in.
$ curl -d wstoken="$TOKEN" -d wsfunction=core_enrol_get_users_courses -d userid=1451616 'https://moodle.org/webservice/rest/server.php?moodlewsrestformat=json' | python -m json.tool
[
    {
        ...snip...
        "fullname": "Moodle in English",
        "id": 5,
        ...snip...
    },
    {
        ...snip...
        "fullname": "Moodle en fran\u00e7ais",
        "id": 20,
        ...snip...
    },
    {
        ...snip...
        "fullname": "Moodle Certification",
        "id": 48,
        ...snip...
    }
]
Recap'
Pre-requisites:
- The Mobile App webservices must be enabled
 
- The REST protocol must be enabled
 
- You need an API token
 
Querying:
- Requests are made to 
YOURHOST/webservice/rest/server.php?moodlewsrestformat=json. 
- Requests must be 
POST requests 
- Requests must contain 
wstoken: Your token 
- Requests must contain 
wsfunction: The function you are calling 
- Requests type must be: 
application/x-www-form-urlencoded 
More
I've greatly simplified how this works and what alternatives there are, but this should get you started. You will likely be interested in looking at the developer documentation to get more information about the available web services: