In this article, it is stated that latency does not affect bandwidth, but insufficient bandwidth can reduce latency.
Can someone explain me the latter part of the statement? How would insufficient bandwidth reduce latency? Is this true?
First, the linked article contains several poor approximation and is not IMHO a good source.
Back to the question, insufficient bandwidth leads to link congestion, that means that the equipment buffers will be full and so some packets will be delayed, waiting for their turn to be sent from those buffers, thus increasing latency.
The author of your reference article does not appear to fully understand or clearly illustrate the relationship of Bandwidth/Latency.
Latency doesn't affect bandwidth, but insufficient bandwidth can reduce latency.
This statement from your reference could be more accurately stated as:
Changes in Latency or changes in Bandwidth will affect the amount of time required for a set of data to travel from point A to point B.
I recommend reading O'Reilly's Network 101, Primer on Latency and Bandwidth for a reference on this topic.
O'Reilly defines Latency and Bandwidth as follows:
Latency - The time from the source sending a packet to the destination receiving it
Bandwidth - Maximum throughput of a logical or physical communication path
To put it another way-
Imagine that you have an entire library of books to transfer to another library. Your data set is the books that need to be moved. You can transport the books on trucks. The trucks represent a packet. The road represents the network. The speed limit and traffic lights represent the latency on a particular road or transit medium. The number of lanes on each road or maximum number of trucks that can drive simultaneously represent the bandwidth.
Increasing the speed limit or independently using a 10-lane highway to transport the books may get the books to the new library faster. However, changing the speed limit did not widen the roads, nor did widening the road change the speed limit.
Which gets ten trunks full of books to the new library faster? One truck that can be sent to arrive every 10 minutes or 10 trucks that take 100 minutes to arrive? Both will get ten trucks of books to the new library after 100 minutes. Which is better? That depends on the type of traffic and situation.
The literature goes into the concept deeper with some detailed examples.
If you reach equipment limits, or limit of your connection, as JFL said congestion occurs. On different media, running different protocols, this is solved on different ways but will increase latency of packet propagation.