Let's say you had a class that you wanted to use, but there was some sort of error in creating the object. This might be that the wrong parameters were passed, or the third party service (eg. a database) wasn't available at the time of creation.
Using frameworks to handle the authentication of your PHP application is perfectly fine to do, and normally encouraged. They abstract away all of the complexity of managing users and sessions that need to work in order to allow your application to function.
A sparkline is a very small line graph that is intended to convey some simple information, usually in terms of a numeric value over time. They tend to lack axes or other labels and are added to information readouts in order to expand on numbers in order to give them more context.
If you've ever looked at the settings in a digital camera, or have experience with image processing programs like GIMP, then you may have seen a colour histogram. This is a simple graph that shows the amount of different shades of colour are present in the image.