ArcGIS applications are built with the assumption that the feature's geometry follows certain specifications. When the processing algorithms encounter data that does not follow the specifications, the software can perform poorly, generate errors, crash, or the operation may succeed without an apparent problem but generate incorrect results.
Origins of invalid geometry
A shapefile is an open format with a documented specification. Many software packages support writing to this format. However, some software packages—sometimes due to bugs, sometimes due to lack of knowledge—do not follow the documented specification.
When shapefiles are loaded into a geodatabase, the features' geometries are copied as they are (with any existing geometry problems), so the same precaution that is needed when using shapefile data must be taken into account when using geodatabase feature classes. The exception is when the data is loaded into an enterprise geodatabase using an ArcGIS client application. Geoprocessing tools (including, but not limited to, Export Features, Feature Class To Geodatabase, and Append) will check and repair the feature's geometry as part of the loading process.
DBMS systems provide native geometry field types. These types of fields can be uploaded and modified through manual SQL expressions or from other software packages. These systems can create geometries that are invalid for ArcGIS.
Responsibility
The responsibility is on the data consumer to ensure that the feature class contains valid geometries before the data is used for projects or analysis. Once the Check Geometry tool is run on a given dataset, you do not need to run it again until the data is modified.
Find and fix geometry problems
The Check Geometry tool generates a report of all features with geometry problems in the feature classes. To fix these problems, use the Repair Geometry tool. See the particular tool's documentation for details on what these tools do.