I like both of the definitions given so far very much.
To me, commitment comes in levels. There's commitment to a relationship with a person, which the other posters have summed up very well, and which I feel for my two partners. I know that I will keep on working to be with them and building what we have unless there are really major changes in our lives that make that impossible.
I feel more committed to Gia than to Davis at present because I can't see those changes, the kind that could lead us to move apart, coming from within me with Gia, whereas I'm still feeling my way towards that place with Davis, if that makes sense. My relationship with him now is very different than those I've had with fwb's where there was no commitment, and we could split apart at any moment without it being a very big deal, but I also don't feel that I've given my full commitment to our relationship yet.
The higher level of commitment, in the way that I think of it, is committing not just to the relationship but to intentionally building a life together, creating a primary partnership. As much as I believe in and honor the commitment that Gia and I share, I know that her commitment to her life partner, the person with whom she's bought a house and had a baby and to whom she's married, is on a different plane than what we have. I see it as taking a greater order of trust and faith and will to choose to cleave to someone in that way and tie all your hopes and fortunes to theirs (assuming that you're really thinking about what you're doing).
It's an interesting topic.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.