This commonly used expression hails from army days when in war, one adversary crosses a river and once their troops arrive on the far bank, burns the bridge behind them to prevent further enemy attack. There is a natural consequence to this tactic: Your team is now trapped on the other side with no route of return.
Keep your resources and network opportunities intact
A parallel can be drawn to career decision making. Whatever stage you are at in career transition, you never want to burn your bridges. The future is unpredictable: You may need to draw on your resources and network opportunities, and it's important to keep them intact. Always take the high road and end all interactions on a positive note.
Maintain your composure and handle the situation gracefully
As an example, a 22-year-old youth I assisted felt he was being taken advantage of by his manager, a self-employed marketing consultant. He was working long hours as the computer technician and the wage (often paid late) didn't reflect his value or the market standard. After six months of productive employment, he felt validated and approached his manager with his concerns. After pondering his request, she offered him an increase if he was willing to work for 6 months unpaid with the promise of a retroactive raise. I commend his actions: He calmly went to his cubicle, packed his few belongings, handed in his resignation and walked away. The youth might have burned his bridges and left a negative lasting impression—commonly called career limiting or career ending moves. Instead, he maintained his composure and handled the situation gracefully as a professional.
Career sectors can be small and word gets around. Always leave at high tide—you never know when your paths will cross again, and you can hold your head high while traversing that bridge.