The Paleolithic Era is significant because people established the process of hunting-gathering, which has supported humans for the majority of their existence on earth. Their means of survival was not altered until the Neolithic Revolution (also called the Agricultural Revolution), which occurred in about 10,000 BCE, when humans started developing settled agricultural techniques. The change towards settled existence and the development of more complex agricultural techniques began following the last Ice Age about 16,000 years ago. After this point, food and animals became more abundant, moving some societies towards the Agricultural Revolution.
In addition, during this era, people started spreading from Africa to different areas of the globe about 100,000 years ago, including to Asia, parts of the Pacific Australia, Europe, and the Americas. This migration set the stage for later development and peopled much of the globe.
The Paleolithic Era also involved the development of simple tools, including the hand ax, and tool-making industries. These industries showed specialization and involved industries concentrated in particular areas, which would lead to even greater complexity in manufacturing in later eras. In addition, in this era, people began creating cave paintings and making sculptures, starting different means of expression that are still important to human beings.
I agree with most of what pohnpei397 has written, particularly the need to discuss this from different perspectives.
The Paleolithic is more than just a foundation for world history. 95% or more of all human history took place in the Paleolithic.
This puts into perspective not only the enormous amount of time that humans have been on the Earth and not resembled our current level of technology and civilization, but it also emphasizes just how rapidly we have developed those things and how exponential our growth has been.
You might have heard of the Stone Age; sometimes this term is incorrectly combined or conflated with the Paleolithic. In fact these are just two ways of categorizing human archaeology; the name "stone age" emphasizes the technology we were using, whereas the Paleolithic covers all aspects of human history and evolution during this time period. One significant element of technology in this period is the fact that homo sapiens didn't invent tools or the use of controlled fire; instead they inherited them from other hominid ancestors and improved them.
While modern human history is sometimes correlated with the invention of agriculture, which didn't take place until the Neolithic, there were still many incidences of human development that we normally consider "modern" which had already taken place in the Paleolithic. Relatively complex societies and languages were developing, along with art and crafts, and possibly cooking outside of the roasting of meat.
Another significant development during this period was the migration of humans around the world, and the end of the last Ice Age period altering the climate.
In terms of relevance to world history, the Paleolithic could be considered the dawn of modern humans, and the beginning of our history as a species.
This is the sort of question that would do better as a discussion since different people can have different opinions about it.
I would argue that it is very difficult to identify any way in which the Paleolithic Era is directly relevant to our history. Of course, it is very important in one sense. It was during the Paleolithic that human beings were coming to develop the sorts of technologies that would eventually allow them to engage in things like agriculture, thereby creating civilization. In that sense, the Paleolithic was an important foundation for our history.
However, the Paleolithic does not really have much in the way of relevance for how human history played out, for what countries became powerful or for what ideologies became dominant. In that sense, it is not very significant in world history.