* A standard degree: This might simply mean a typical undergraduate or postgraduate degree (like a Bachelor's, Master's, or PhD) in a particular field, as opposed to something unconventional or specialized.
* A degree in a common field: Someone might call a degree in a widely pursued field (e.g., Business Administration, Engineering, Education) a "normal degree" compared to a less common one (e.g., Egyptology, Astrophysics).
* A degree without distinction: In some systems, degrees can be awarded with distinctions (e.g., first-class honours, second-class honours). A "normal degree" might imply a degree without any such distinction.
* A degree from a mainstream institution: This might be used to contrast a degree from a well-known university with one from a less established institution.
To understand what someone means, you'll need to consider the context in which they used the phrase.