Customer or Client Relationship Management (CRM) is an approach to manage your company's interaction with current or potential clients. CRM systems typically include a centralized contact manager system that integrates detailed user profiles, emails, marketing automation, scheduling, tags, and ecommerce capabilities.
We have done an overview of how these systems can work together here.
There are many CRM standalone components available in the marketplace and it is possible to put together different systems to match the functionality of more integrated systems like Infusionsoft, Ontraport and ActiveCampaign (see below).
For example, simple contact management and email marketing can be performed using popular programs like MailChimp and Constant Contact. eCommerce support can be done using WooCommerce and many WordPress templates come with integrated WooCommerce template support. One of our clients uses and recommends Less Annoying CRM.
We use Infusionsoft which provides a highly integrated system but it is very complex to use fully and may not be the right fit for a small business (and it is not cheap!). To address the complexity and steep learning curve to use Infusionsoft, they have now released a cheaper and lighter version called Keap. Competitors in the InfusionSoft/Keap space include Ontraport and ActiveCampaign. Here is a good comparison of the features of these 3 systems (released before Keap was available).
One of the reasons that you may be considering a more robust CRM system is to control access to specific content in WordPress. There are a number of WordPress extensions or integrations (called plugins) that allow you to map categories of users in your CRM (e.g., 'clients') to WordPress resource access rights. For example, we have a group of users in CRM who are tagged as our 'STELLAR' or 'ELITE' clients which means that they have access to a specific set of resources on the BusinessGrowthAcademy.com website. The alternative to an integration with your CRM is to manage these access rights (aka Memberships) completely in WordPress using a tool like MemberPress.com.