I'll do my best to give a brief summary below as well:
Essentially, the people core service contains various services that allow you to deploy a cross-solution identity (MCID) that will allow you to use the best parts of each solution together. For example, you can deploy A4T which allows you to use the powerful Reports and Analytics interface and tools to analyze Target activities. You can use Experience Cloud Audiences to build complex segments in Analytics for use in Target activities to create powerful experiences for your customers. Additionally, you can use Customer Attributes which allows you to take your offline data from a CRM system and match it up with your Adobe data for reporting or experience Targeting.
Please let me know if you have additional questions.