The most important impact of the Cariboo Gold Rush on British Columbia was that the gold rush helped cause the development of the province. All sorts of infrastructure was created to facilitate the exploitation of the gold deposits that were being mined during this rush.
Before the gold rush, BC had very few people and very little in the way of roads and towns. The gold rush changed this. Because of the rush, towns sprang up. Roads and bridges were built. Steamboats were brought to move goods up and down rivers. The government presence in the province increased greatly. In short, the demands of the gold rush led to the creation of a real infrastructure and to the start of a large permanent population with a real government in what later became the province of British Columbia.
The Cariboo Gold Rush of the early 1860s was, unlike the earlier Fraser Canyon Gold Rush, a primarily Canadian gold rush. Although Americans were present in the first wave, the later parts of the gold rush were primarily Canadian and led to settlement within the interior of what was then the Colony of British Columbia. This settlement would trigger later gold rushes, as more gold was discovered in the interior. After the gold rush ended in the 1880s, many of the settlers turned to ranching.
In addition to encouraging interior settlement, one of the changes the gold rush caused in British Columbia was the construction of the Cariboo Wagon Road. The road resulted in bringing needed infrastructure to the colony as well as increased regulation of the gold rush area by the government. The Royal Engineers who built the road constructed other forms of infrastructure, such as the Alexandra Suspension Bridge. The road was so costly to build that it forced the colony into a union first with Vancouver Island in 1866 and later with the Canadian Confederation in 1871.
First and foremost, it is important to note that British Columbia experienced two gold rushes. The first one took place in 1858 after gold was discovered on the Fraser River. The second one which occurred in the Coriboo district and which is the subject of this question took place in 1862. Due to the influx of people into Cariboo including immigrants from as far as Germany and China, all of whom had come to chase after the gold fortune, famous towns such as Barkerville, Richfield and Keithley Creek sprund up and there was increased development in the mainland.
In addition to the towns, infrastructure was improved in order to ease the movement of people and materials that had prior been done amid great difficulty. It began in 1859 when James Douglas gave a nod for the construction of a 4 foot wide trail known as the Douglas Trail that connected the coast and the interior. Later on, the construction of the Cariboo Wagon Road made transport more efficient as it facilitated the use of wagons that hastened the transport process.
British Columbia experienced an economic boom due to the mining activities going on in its interior. The establishments that provided them with food, accommodation and other supplies before they proceeded to the interior benefited a lot. This opened up British Columbia to settlement by people of non-Aboriginal descent. In summary the Cariboo gold rush improved the economy and infrastructure of British Columbia while at the same time diversifying the population.