Having vector data without topology errors is important for further analysis, as these errors may lead to incorrect results.
This recipe shows you how to use the built-in GRASS tools to fix various topology errors in vector layers.
QGIS has very good integration with GRASS GIS; there is a GRASS plugin that provides access to the GRASS GIS database and functionality. GRASS algorithms are also available from the Processing plugin. The latter is simpler because you don't need to bother with setting up GRASS locations and mapsets and importing and exporting data.
To follow this recipe, load the nonbreak.shp, dangles.shp, and nosnap.shp layers from the sample data. Additionally, make sure that the Processing plugin is enabled in Plugin Manager.