The main thing with LTI™ is the identity assertion. LTI is a way for one system (the tool consumer, typically an LMS) to send a user to another system (the tool provider, some service that integrates with the LMS) in a trusted way. The most common reason for the trust assertion is to allow the user to be automatically signed in and directed to a specific course or module when the provider renders content.
The consumer and provider have a predefined relationship via a consumer key and shared secret which are used to sign any messages passed between systems. All messages are signed with an OAuth signature that can be verified by either party. Generally information only travels one way, from the consumer to the provider.
Here is a list of parameters that can be sent as part of the POST request. Some are required, some are optional. Most apps should not need more than the first set of parameters and most likely will ignore the rest.