"An election" would be for one office. "Elections" would be for multiple offices, or for the same office on different occasions.
So: "Mr Jones won the election for senator." He ran for this office and won.
"The Foobar Party swept the elections." There were many offices, and the Foobar Party candidates won some large majority of them
"Mr Jones has won all the elections he's been in." Mr Jones has run for many offices over the course of his career and he has always won.
"We have elections for president every 4 years." It's a recurring event, so there are many of them. You could also say, "We have an election for president every 4 years." That would mean the same thing. Side note: "1 to 4 years is the frequency of elections" is, I guess, technically correct but it's awkward wording. It's not the usual word order.
You could say, "We hold elections every two years." Depending on context, that could mean that there is some office that we're holding an election for every two years, not necessarily the same office. Like in 2010 we have elections for mayor and senator, in 2012 we have elections for governor and sheriff, etc.
I think people often say "election" to mean one trip to the polls as opposed to one office. Like, "Did you vote in the last election?" is pretty much the same as "Did you vote in the last elections?"