For example, if you look at a map of the world, you will notice that the UK is at roughly the same latitude as some of the northernmost parts of Canada but is much warmer. This is partly due to the warm waters brought by the Atlantic's "conveyor belt" to the waters surrounding the UK's coasts. If these warm waters stop flowing toward the UK, its weather would likely evolve to resemble that of northern Canada.
There are other complicated factors and feedback loops involved, but this example should give you an idea of how important this Atlantic current is to the stability of global climate.
[a] https://www.amazon.com/Ice-Age-John-Gribbin/dp/1511926422[b] https://en.wikipedia.org/wiki/Glacial_period