API Version - Specifies which service is being requested.
v2 - This is the service that executes scripts stored in the integration point library.
Database - Specifies which database contains the script.
master - This database requires the credentials to be provided.
Script - Specifies the name of the script contained in the database. The SPE module containing the script needs to be enabled otherwise you'll receive a 404 error.
homeanddescendants - Replace this name with whatever your script is called in the Web API library.
Query String Parameters (deprecated) - Specifies the additional bits of data for use by the web service.
user and password - Authenticates the request and in most cases will be needed. If the script is published to the web database the credentials are not required. You should use the Basic header instead of the query string.
All of the query string parameters added to the variable scriptArguments. Use this PowerShell hashtable inside of your scripts. Check out the function Invoke-ApiScript for an example of how these parameters can be put to good use.
Use the Basic header to provide authentication information. Here is an example of how to build that for a script.