Dot notation
FQL is all about getting data from the inside of a tree structure, into a new form, most of all table form. And it uses the power of FhirPath to do that. FhirPath is a language developed as part the FHIR standad, to get values out of FHIR resources. And FHIR Resources are trees.
Descending
FhirPath uses a syntax very common to many programming language: it uses dots do drill into (or descend into a structure. The official term for this is dereferencing. Look at this FhirPath statement
Patient.name.given
It drills from the root of the tree, the Patient, into the name of the patient, and after that into the given part of the name.
Multiple branches
Since each descention, can result into more than one branch (a patient can have more than one name), each descent, leads to more values.
So Patient.name gives you back all the names of the patient, and name.given gives you back all given names of the patient name.
And so Patient.name.given gives you all givens of all names of patient.
Optional Resource name
In any FhirPath statement it is optional to add the root of the path - the resource name. So the following statements produce the same outcome:
Patient.name.given
name.given