I guess a good example would be Fun Home. Last year three actresses were nominated from the show in the same category: Sydney Lucas, Judy Kuhn, and Emily Skeggs. Also in the category were Victoria Clark (Gigi) and Ruthie Ann Miles (King and I). For purposes of this, we are going to exclude Victoria Clark.
Say there are 100 voters (the number this year is roughly 777, but 100 is a prettier number). The term "to split the vote" means that instead of voters just being able to go "I'll vote for the actress from Fun Home", they now have to decide which of the three they are voting for, essentially lowering the numbers each actress receives.
Say, if only Sydney was nominated (and Ruthie for purposes of this example), a vote could look like this:
Ruthie Ann Miles: 40
Sydney Lucas: 60
And Sydney would win.
However, if we put all three Fun Home actresses in the category and keep Ruthie's votes constant (though this is unlikely in real life as some voters would most likely switch), it may look like this:
Ruthie Ann Miles: 40
Sydney Lucas: 28
Emily Skeggs: 12
Judy Kuhn: 20
*note - I'm using a random split of numbers, not my personal beliefs.
And therefore, Ruthie would (and did) win.
Did that make sense and/or answer your question?