This goal has to do with the character getting out from under the financial protection of others and being able to care for themselves. The character seeking this goal could be a spouse or lover who no longer wants to be monetarily provided for, a young adult leaving the nest and seeking to support himself, someone in poverty taking steps to improve their financial situation, a captive wanting to escape their abuser, a mentally challenged person striving to become financially independent of their caregivers, or anyone else who wants to stop relying on the monetary support of others.

Getting a job
Going back to school to gain education that will lead to a better paying job
Seeking knowledge that will help one manage one's finances appropriately
Seeking out a second job to supplement one's income
Monetizing a skill or talent to earn a living (selling one's handicrafts, seeking publication for one's writings, teaching others to paint, etc.)
Relocating to a place where one will have more freedom and opportunity to find work

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Self-Actualization: If a character sees their ability to support themselves as a means of improving themselves or becoming a better person, that need to be fully actualized could drive them to pursue that goal.
Esteem and Recognition: While many caregivers financially support their charges out of love, some do so because they want to control the character or keep them from leaving. In this case, the financial "support" becomes a means of oppression. A character in this position will likely feel a lack of esteem for themselves. One this lack becomes critical, they may strive to break free.
Love and Belonging: A character who wants to show their love for someone else by supporting them will first need to be able to support themselves. In this way, the need for love and belonging can motivate the character to become financially independent of others.
Safety and Security: One of the roadblocks to an abused or captive character becoming free is their ability to earn their own money. If their safety is threatened by their situation, they may be driven to pursue this goal.
Physiological Needs: The basic physiological needs of food, water, and shelter must be obtained and maintained with money. Without them, a person's very life is in danger. When the situation becomes critical for the character, they may be pushed to take steps toward this goal.