Foster means to stimulate, support, sustain or incite something. The term comes from the word "fomento" (from the Latin “fomentum”, which means “warm”), a remedy used to rub the skin. In this context, fostering is the act of rubbing the skin with liquid medicine for therapeutic purposes.
In a figurative sense, fostering is stimulating something, adopting the necessary means and care to promote development and achieve positive results.
In Economics, the act of fostering is related to creating policies to drive the progress of something, for example, fostering entrepreneurship will result in the creation of new companies, new jobs, greater dynamism in the economy, etc.
When a politician says that he is going to boost the city's economy, it means that he intends to promote the local progress, putting into practice strategies for the development of the region and favoring the well-being of the population.
The meaning of fomenting can also be used in the sense of motivating, originating or inciting a reaction. For example, fomenting hatred, fomenting discord, etc.