The doctrine of the Trinity is a tricky one - God is three and one, wait, what? How does that work? As a result, it's one of the doctrines with the greatest potential for heresy. One of the heretical ways of speaking about the Trinity is modalism, which is basically the idea that God is one God but has three different ways of being God. Meredith Brooks' song 'Bitch' is a good example of modalism:
"I'm a little bit of everything all rolled into one
I'm a bitch, I'm a lover I'm a child, I'm a mother
I'm a sinner, I'm a saint I do not feel ashamed
I'm your health, I'm your dream I'm nothing in between
You know you wouldn't want it any other way"
This is, I think, a modalistic account of selfhood: I can be lots of different things, apparently all at the same time. One minute I'm nice, the next I'm nasty, and all of those different ways of being are equally part of who I am.' She's talking about herself, so it's not exactly heretical, but this is actually precisely the problem with the doctrine of the Trinity: the only resources we have for understanding it come from our own experience, and there isn't anything in our own experience which quite fits with the idea of a being who is entirely one and entirely three.
Some modalists have related the trinity to the process of human history: in the Old Testament, God related to us as Father; in the New Testament, he related to us as Jesus; in the era of the Church, he relates to us as Holy Spirit. It's the Clark Kent model of theology: God takes off his glasses and puts his underpants over his trousers and ta-da! He's no longer the Father but the Son!
Not only do most forms of modalism violate the principle of opera trinitatis ad extra indivisa sunt, but it leaves you with a God who's basically one being with different moods. Too much oneness, not enough threeness = trinitarianism fail.