It took humans 10,000 years to learn how to grow most of the crops we now take for granted. Along the way, we despoiled most of the land we worked, often turning verdant, natural eco-zones into semi-arid deserts. Within that same time frame, we evolved into an urban species, in which 60% of the human population now lives vertically in cities. This means that, for the majority, we humans have shelter from the elements, yet we subject our food-bearing plants to the rigours of the great outdoors and can do no more than hope for a good weather year. However, more often than not now, due to a rapidly changing climate, that is not what happens. Massive floods, long droughts, hurricanes and severe monsoons take their toll each year, destroying millions of tons of valuable crops. Source: http://mini-ielts.com/386/view-solution/reading/crop-growing-skyscrapers
You can see what it's saying by taking the end of the sentence and substituting it in to the "more often than not."
[that is not what happens] more often than [that is not what does] not [happen].
As you can see, there is a double negative which really makes this sentence confusing. As for what "that" is talking about, the previous sentence reveals that it's talking about good weather. So the "more often than not now" is saying:
[Good weather is not what happens] more than [bad weather does happen]
[Bad weather happens] more than [good weather does] not [happen].
Basically, it's saying that our hope that there would be good weather for our crops is not a sound hope.