These terms are company and environment.
In simplistic terms, a company is a container which holds all information (setup, master and transactional data) for a legal entity. If we have a company called Cronus which has operations in England and Scotland, they might create two companies as there are two legal entities which operate under different legal jurisdictions.
These two companies would exist in the same environment. Environments are used to separate production systems from development or testing systems. While you can have a test company on the production system, there is a risk that emails could be sent from the test company to a live client.
To mitigate this risk, Dynamics BC allows the creation of a sandbox environment which allows for testin of new processes or features without risking the live system.
Multiple environments might also be used if you have mutiple companies operating in multiple countries as an environment is liked to a country (England and Scotland, which I mentioned earlier, are a special case as they are both part of the UK, which Dynamics BC would regard as one country).
When you sign up to Dynamics BC for a trial there is one environment and two companies automatically created; a Cronus sample company with sample data and a new one called My Company which is a blank company.
If you have more than one environment you need to specify the environment you want to access during login.