There are a wide variety of vector formats with quite distinct purposes. Some of the vector formats are created to fully support the specialities of the host software while others are more general ones. A unique property of vector GIS formats is that there isn't an all-purpose, all-in-one format. There are two main types of formats--binary and ASCII (text-based). Binary formats are more concise; however, they require parsing algorithms with binary magic directly developed to support them.
ASCII formats, on the other hand, are human-readable and some of them (like JSON and XML) are natively supported by several high-level programming languages (especially, fourth-generation languages). Others can be interpreted by easily implementable string manipulation techniques.
We can export layers from QGIS by right-clicking on their items in the Layers Panel and selecting Save As. In the dialog, we can not only specify the new file's destination, name, and format, but we can also save only selected features (if there are any) by checking the Save only selected features checkbox. If we would like to exclude one or more of the attribute columns, we can expand the menu Select fields to export and their export options and specify the columns that we would like to export. Finally, we can also specify a very important property of the vector layer--its CRS. If we select a CRS different from our layer's, QGIS automatically transforms our features to the selected destination CRS.