Why would a European man or woman sign an indenture that committed them to be a servant in America?
In fact, many indentured servants who came to America did so because they had no other choice. Although for many the prospect offered a new beginning (Benjamin Franklin's grandmother came as an Indentured Servant and married her master,) for others the choice was between servitude or prison for debt. Many did not come voluntarily; rather they were given the choice of prison or servitude. Of those given the choice, many chose prison, as tales of the horrors of the life of a servant in the colonies were rampant.
The promise, of course, was of land at the end of servitude; but many had never worked land and had no farming experience. So the reason for their coming to America was either desperation or fear of a worse alternative.
Of course, there were many different reasons for Europeans to sign up to become indentured servants. However, the general reason was that they felt they would have a chance at a better life in America than was available to them in Europe. A European who made it to America as an indentured servant could hope for a better future. He or she would, after a period of years, be free in a place where there was more land and more economic opportunity to be had. This made it, for many, worth the years of servitude.