The term "PSQ" is frequently used on Mathematics Stack Exchange, both on the main site and meta. For the benefit of users unfamiliar with this term, I thought that it would be a good idea to ask here:
To answer the first question, the acronym (or some might prefer initialism) PSQ, is derived from Problem Statement Question.
In its purest form it is a question post that only contains the statement of a problem, in a form that is frequently found in exercise sections of textbooks, assignments and alike, e.g.:
Prove that $\sum_{i=1}^n i= \frac{n+n^2}{2}$ for each $n \in \mathbb{N}$.
This is, grammatically, not even a question. By extension the term PSQ is used to name questions that are very reduced and lack all context, e.g.:
How can one prove that $\sum_{i=1}^n i= \frac{n+n^2}{2}$ for each $n \in \mathbb{N}$?
To answer the second question, a problem with this type of question is that they are poorly scoped. It is not clear what answer is sought. The default assumption is that a poster wants a solution that makes sense in the context in which such a problem usually comes up. However, this is inherently vague and actually not always the case.
For the example I gave most will assume (and to be sure they will be right many times) that a proof with reasonable detail showing the equality by induction will be a good answer.
However, it is also possible that the poster does not even know what the symbol $\sum$ means. This is not at all unrealistic, especially if they did not type it correctly in MathJax but instead posted a screen-capture.
There are other problems with this type of question-posts and this has been discussed frequently in the past. The expectation is that question-posts contain context as described in How to ask a good question.
More broadly, the intent is to have questions more in line with How to ask a good question.
A more clear name might be QLC, that is, Questions Lacking Context. Sometimes the very broad term of Low Quality Question is used, but that has its own set of problems to it.
