I came across the notation $A.B$ in many occassions while reading papers in Group Theory. However, I have not yet found any description of what this notation is supposed to mean. From context I suppose it means that if $G=A.B$, then $G$ is a solution to the extension problem $1\rightarrow A\rightarrow G\rightarrow B\rightarrow 1$, and the extension is not necessarily split. Is this the right way to interpret this symbol? In that case I suppose it would be useful in cases where the analysis does not depend on the particular extension.
This is known as ATLAS notation, and it was introduced and widely used in the ATLAS of Finite Groups. It has become a standard notation among (particularly finite) group theorists, and it is very concise and useful, but it should be used with care.
In fact you have guessed the meaning correctly. If $A$ and $B$ are groups (or isomorphism types of groups), then $A.B$ means any group with normal subgroup isomorphic to $A$ with corresponding quotient group isomorphic to $B$.
There are refinements. For example $A:B$ denotes a split extension, and you would normally use $A \times B$ if you knew that it was a direct product, but just writing $A.B$ does not imply that it is not split or a direct product, it probably just means that you do not know or care.
Other conventions include using a number to denote a cyclic group of that order (as in $3.A_6$or $A_5.2 = S_5$), or a number like $$ in square brackets to denote an unspecified group of order $12$.
In addition to Derek Holt's answer I am adding here a reference to a webpage by Tim Dokchitser that explains the ATLAS notation
Edit: Thanks to Derek Holt who clarified the difference between the notation $A.B$ in the ATLAS and the page above. In the ATLAS $A.B$ is an arbitrary extension, whereas in the webpage it denotes a non-split extension.