I am reading a scientific article and it says that something is not at variance with something else; can anyone tell me what it is meant by saying not at variance please?
Of things, "at variance" simply means in conflict, at at least a state of difference. If two things are "not at variance with" one another, then they are in agreement, or at least not mutually exclusive.
The exact same sense can be applied to people, although it will often be in regards to a particular issue: two people at variance over a bill, for instance.
Since you say you encountered this in a scientific paper, I think it's worth pointing out that this meaning and use of variance has nothing directly to do with statistical variance. There are two classes of definition for variance, one simply refers to variation or repeated change, often over time, but sometimes over another factor. This sense includes the technical definition of statistical variance.
The other class (which includes the usage in the question) refers to differences between separate things, ideas, or people--meaning "at odds" or "in conflict" or simply "not in agreement". This sense, though somewhat formal for casual speech, one might expect to encounter in pretty much any situation.