The noun factor means "one that does" (from Latin 'facere'). We usually employ it to designate one of several driving forces or important parts helping or hindering a process.
The process here is the reduction of global poverty levels. I am certain that you can identify some other factors that play their roles (positive or negative) along with the "wider provision of electricity supplies". Considering that they all take part, often simultaneously, to influence the process' outcome, you can think of them as actors in a play or gears in a gearbox. That's why they are factors in something.
Another way of looking at factors comes from mathematics. A factor is a prime number, often one of several that make up a given number by multiplication. For instance, number 24 is made up from 2*2*2*3. Each of those (three 2s and a 3) is a factor in 24* (because they comprise it).
You can use preposition 'in' with other gerunds like you would with nouns.
My experiences in answering SE questions helped my own growth.
His efforts to answer a question ended in doing somebody's homework.