Paradoxically, this image is a function of bi invisibility. If a bi person doesn't fit this picture, would you ever realise they were bi?
It may mean that supposing they split up with their current partner, they could imagine being with either a woman or a man next.
It may mean that they never imagine splitting up with their current partner, but they still call themselves bi to acknowledge their attractions to people of more than one gender. For some bi people this is politically important; for some, it's more about being true to themself and honest.
Acknowledging the attraction doesn't mean you will necessarily act on it, either now or in the future.
"Learning to legitimate desire without necessarily acting upon it is a challenge any long-term monogamous relationship faces." - Ruth Gibian, 'Refusing Certainty: Toward a Bisexuality of Wholeness', in 'Closer to Home: Bisexuality & Feminism'
Some people use the term polyamory to refer to multiple relationships. (Sometimes including love-relationships that don't become sexual at all, or have been sexual but no longer are; on the other hand, sometimes only meaning relationships that include sex.) Polyamory always means honest relationships, not two-timing or cheating.
Most people seem to consider non-monogamy a wider term than polyamory: polyamory usually implies the possibility of multiple long-term love relationships, whereas for some people, non-monogamy might mean simply having casual sex with more than one partner. On the other hand, some of the people who identify as non-monogamous are doing exactly what others would call polyamory, but prefer (for various reasons) not to use the word.
Multiple relationships can take different shapes. Where one person has two lovers who are not themselves lovers, that's sometimes called a "V". Where three people are each sexually/emotionally committed exclusively to the other two, that's sometimes called a polyfidelitous triangle. (Again, bisexuality need not be implied - it could be three people of the same sex.)
Some polyamorous relationships include lifelong commitments to one or more of the partners involved (such as when someone has two "wives", or two "husbands", even though in many countries such relationships are not recognised as marriages in law).
Not all of one person's relationships are necessarily designed identically. For instance, some people have one partner they call their primary partner and other lovers who are more part-time. Or, for some people, sex can be a possible expression of close friendship, and what happens depends on each friendship.
Most polyamorous relationships include promises which, while not necessarily lifelong, set out boundaries for the relationship. These may include promises about sex (e.g. to practise safer sex with everyone except the primary partner, or to have sex at all only inside declared, committed relationships), promises to be honest, promises to check in with the other person (or people) when making plans, or other agreements.
Some people identify all the time as polyamorous ("poly" for short) because they know themselves to have the capacity for multiple relationships, even though they may currently be with one partner or no partner. People who call themselves poly may nevertheless choose to stay monogamous with a particular person - perhaps because their partner asks them to be monogamous, or simply because that feels right to both people at the time.
Another big factor is whether you're good at listening to others and asking for what you want. Honest communication is vital, as is keeping your promises. Of course, these qualities are at the heart of loving, supportive monogamous relationships too.
Some people feel much more secure in monogamous relationships, so that polyamory may either be practically impossible for them, or seem so difficult that it isn't worth the bother.
Jealousy is not necessarily a sign that multiple relationships would be impossible. Some people use it more as a sign that something needs sorting out. Perhaps someone is not getting enough time, or needs more information to reassure them that another relationship of their partner's won't be at their expense. You may need to work out new boundaries that everyone can live with.
Some people also think of it as a political choice - rejecting the cultural imperative that the only valid form of love/sex relationship is a couple of one man, one woman.
Also, there can sometimes be more emotional stability in, say, a committed triangle, than in a couple. If one person is having a bad time, they have two partners (as well as perhaps friends or family) to support them, and if one pair is arguing, the third person may be able to see clearly what's going on and support them both in resolving the argument. This is not necessarily true of all multiple relationships, though - it depends on the dynamics of each one, and how well the different partners know each other.
When you're getting what you need yourself, it can be very joyful to see someone you love being happy with someone else. This feeling of benevolence, love and enjoyment is known as compersion or being "frubbly".
Of course, there are also people in the world who cheat on their partners, and there are still people who practise non-monogamy in a way that doesn't work for their partners. But they should not be taken as representing the whole genre of non-monogamy. There are honest and dishonest ways to do these things, and thoughtful and thoughtless ways, and the honest, thoughtful ways can work extraordinarily well.