Cabinet
A cabinet is an enclosure for housing your equipment with pre-drilled holes (or squares) along a 4-post support system for mounting equipment. When you look at the specs for a cabinet, it may list the inches or centimeters, but in the data center industry, the important specification is called U, or Rack Units. A rack is something different (see below), but the unit of measure is the same between a cabinet and a rack. The most common size for a data center cabinet is 42 rack units, or 42U. Not all 42U cabinets will have the same exterior dimensions - what the 42U refers to is the inside height, and there are various options that may extend the width or depth of a cabinet by varying amounts. Most cabinets today have an outside footprint of 24" wide by 42" deep, but just 10 years ago it was nearly unheard of to have a cabinet with a depth greater than 36". As hardware evolves, so does the infrastructure.
Point of Demarcation / Point of Entry
Depending on your fault tolerance design, this will be one or more locations in your facility where your service providers (electrical utility, ISP) enter and then terminate into some device that allows you, the customer, to extend that service as needed. In other words, it's the point where your utility no longer worries about the physical infrastructure. If you have designed your facility to be concurrently maintainable, there would be a minimum of two separate points of entry to your facility for all utilities.
Rack
A rack is actually referring to infrastructure that was very commonly found in telecom closets and central offices - it is a 2-post system designed to house devices that don't need that additional support. As most hardware has gotten heavier since the early 2000s, it is becoming less and less common to see these racks in a data center other than at the point of demarcation.