Definition: "Azure Logic Apps gives you pre-built components to connect to hundreds of services." Reference Logic Apps can be used to automate business process and to schedule key steps within processes to occur at key times or when certain conditions are met.
Logic Apps can combine predefined existing services or components or they allow you to create your own components or services.
Logic Apps work with "Connectors". A connector uses the external service's REST or SOAP API to connect components or services. For instance a connector can call a service's underlying API. There are existing connectors such as a Twitter Connector or a D365 Connector and custom connectors can be created.
Why would Logic Apps be considered in the world of D365 Online?
Take for instance the need to batch process data within a time frame such as every day at 4pm process data from System A, clean the data and push it into a D365 Online Instance. In this particular example Logic Apps can be used to bridge the need to schedule a process from an external system into D365.
There are many other examples as well.
You also have the ability to work with TRIGGERS and ACTIONS within the world of Logic Apps.
"A trigger is an event that occurs when a specific set of conditions is satisfied. Triggers activate automatically when conditions are met. For example, when a timer expires or data becomes available.
An action is an operation that executes a task in your business process. Actions run when a trigger activates or another action completes." Reference
Defining Triggers and actions and creating your Logic App is all done within the Logic Apps Designer. A graphical tool for creating your Logic Apps workflows.
Logic Apps are not always the answer, but are one of the many choices in the world of Microsoft Azure and Microsoft Dynamics 365 for Customer Engagement. Take a minute to read up on Logic Apps using the reference links above. Also for a quick peek into when to use Logic Apps, here is the decision tree. Reference