Non-commercial means something is not primarily intended for, or directed towards, commercial advantage, or monetary compensation by an individual or organisation.
Your use of someone else's work should not conflict with the legitimate interests of the creator of artistic work. This means that the creator should not be prevented from licensing their copyright for a specific purpose, or receive remuneration for use of their work.
Non-commercial licences only restrict what a reuser may do under the licence and not what the licensor (the rights holder) can do. Licensors that make their works available under non-commercial licence are always free to monetise their works. Licensees are always free to contact licensors to ask permission to use the work for commercial purposes.
The concept of fair usage exists within "The Copyright, Designs and Patents Act 1988"; commonly referred to as fair dealing. It's a framework designed to allow the lawful use or reproduction of work without having to seek permission from the copyright owner(s) or creator(s) or infringing their interest.
It is the user's responsibility to satisfy themselves that an exception applies, such as fair dealing criticism and review, quotation, or reporting a current event.
The non-commercial fair dealing exception is allowed if:
1) The purpose of the use is non-commercial research and/or private study
2) The use of the materials is fair
3) The use is made by researchers or students for their use, only
4) Researchers give credit to the copyright holder
Generally, non-commercial use could be:
Use in free educational lectures and classes
Use on an individual or group's website discussing the artwork in question
Use on websites that are primarily information-led, research-oriented and non-commercial