To answer that question it is basically an assigned I.D. to your character information granting the ability of a third party software. To access your information to accomplish a function and or supply your details to a party requesting an API key or user I.D.
For example should you down load a “ship fitting” assistance program for Eve. The key provided will draw information from your account prudent to game skills learned and level of abilities via your “API” key. To provide information as to fits you may or may not use based on your character stats and limitations.
You have to supply a “API” key to use that software to properly give your fit information based on again your EVE skills.
You will be given a user I.D. information upon your API key request.
Log into : https://community.eveonline.com/support/download/
Then select Login
It should be the same information that you use to log into Eve.
Right of the page you will see a “API” management please select.
Hit the “create a API key” or “ create a new API key”
Fill out all the information on the screen you have the option to make this key have a expiration or check the box for “no expiration”.
Below the entry fields you will see boxes with the word “all” in yellow on top. Left click on these to allow in information below to be accessed. Doing this correctly the “all” will change to “none”. Scroll down and click on the right the “Submit” bar. (do not worry about the access mask information bar)
You will be given a “Verification Code” very long so copy and past to a Eve option note pad you should title “API” key. After you save your new “API key” then copy and paste your “Key I.D.” this is your user information.
Now you have the ability to use third party software and should any corporation you are working with ask for a API key and User I.D. your all set up now. Any questions you know I’m always at your disposal.