Active Directory (AD) is a directory service that Microsoft developed for Windows domain networks. It is included in most Windows Server operating systems as a set of processes and services. Initially, Active Directory was only in charge of centralized domain management. Starting with Windows Server 2008, however, Active Directory became an umbrella title for a broad range of directory-based identity-related services.
Active Directory is a database based system that provides authentication, directory, policy, and other services in a Windows environment
LDAP (Lightweight Directory Access Protocol) is an application protocol for querying and modifying items in directory service providers like Active Directory, which supports a form of LDAP.
Active Directory Domain Services is Microsoft’s Directory Server. It provides authentication and authorization mechanisms as well as a framework within which other related services can be deployed (AD Certificate Services, AD Federated Services, etc). It is an LDAP compliant database that contains objects. The most commonly used objects are users, computers, and groups. These objects can be organized into organizational units (OUs) by any number of logical or business needs. Group Policy Objects (GPOs) can then be linked to OUs to centralize the settings for various users or computers across an organization.
When people say “Active Directory” they typically are referring to “Active Directory Domain Services.” It is important to note that there are other Active Directory roles/products such as Certificate Services, Federation Services, Lightweight Directory Services, Rights Management Services, etc. This answer refers specifically to Active Directory Domain Services.