Events can have a Label and a Custom Data object attached to them. Both can be later used for three purposes : 

Labels are a simple way to attach an extra piece of information to an event. For example, a common case is the name of the visited screen attached as a label to a "visited_screen" event.

You can use labels to improve your user segmentation: 

Or as an additional filter to trigger a push campaign:

Or else, as an additional filter to trigger an In-App campaign:

You will find more information on labels here: iOS / Android / Cordova / Flutter / React Native

In case you need to send more information on a user action, you can also attach up to 15 attributes and a tag collection (containing up to 10 values) to your event. 

This is useful when you need to collect several pieces of information on the same action. For example, if your app is selling package holidays, you probably want to track the following information each time users search for an offer:

Data sent in that format will be useful to improve your campaign's targeting and to add an additional filter to trigger a push campaign, but you won't be able to use them as an additional filter to trigger In-App messages.
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You will find more information on custom data tracking here: iOS / Android / Cordova / Flutter / React Native

You can use the debug tool to check the data Batch has on your install and make sure you have tagged your app correctly: How can I see the data attached to my install or user ID?