The idea behind this motto is that problems should be approached from the perspective of those who face the problem, rather than from an outsider's view of it. The principle is that anyone looking to impact the situation should work to do so in a way that is both
Thinking like the problem means to consider the needs of someone who could as easily be our neighbor as a stranger in another land, instead of looking at the situation through our own lenses. This lens is usually influenced by anecdotal evidence or media representations. Simply put, look at the problem as if you are in the fishbowl that is experiencing it, not from your own fishbowl.
Working like the solution means to come up with an other-fishbowl-centered solution that works and is ongoing. Look for ideas as if you are the one enduring the problem, not as if you are helping someone else. In other words, donating food for temporary relief is not as sustainable as financing an agricultural or educational program that will feed people for years to come.
Ultimately, in working to solve global problems, we should not do it as "charity tourism," which is often temporary and from an outside-in viewpoint, no matter how positive it is. The danger is that the positive impact could be centered on the person doing the work, rather than the person getting the help.
For example, a person who goes to a another country to work on a charitable project probably also sees the sights, enjoys the local cuisine, and posts to social media about what a "transformative experience" it is, as a tourist does. The resulting work might not be as long-term as if that person had instead researched a problem that the village has, then used the time, energy, and efforts at home to raise money and support for a sustainable solution based on what the people abroad need most.
Further, in traveling to foreign lands to solve foreign problems, people might be neglecting the opportunities for service in their own communities. Given the common problems people face, one could just as easily work on providing high-quality education, or clean water, or medical care, or any number of other goals to people in another zip code rather than another time zone.