The EVE Online API system allows information to be retrieved about your character and account without the need to log into the game.
There are many unofficial third party applications developed by players for the benefit of the community. Such applications help you plan your skill training, tinker with ship fittings and keep an eye on your industry jobs. However you cannot make changes through the API system, it is only used for reference.
In order for information to be retrieved you will need to produce an API key. It is important to remember that if you provide your API key to someone then they may be able to pull information about your character including your mails, skill points, contacts and also when your account expires.
The API key will not be able to pull information about your account username or password.
To create an API key you will need to log into your API management site which can be found at:
https://community.eveonline.com/support/api-key/
Click on the 'CREATE NEW API KEY' button. You will then need to select which sections you wish the API to be able to pull information from. Once you have selected a section give your key a name and then click the 'Submit' button.
If your key shows an 'Access Mask' of 0 then it means you have not selected any sections.
To determine what information the key needs access to please consult the documentation of the application you wish to use it with