背水の陣 literally means “a position with one’s back to the water”. However, the best English translation would be “to burn a bridge (or boat).” We use 背水の陣 when we to drive ourselves to a corner as a tactic or strategy.
This phrase originates from China, particularly during the Battle of Tao River, which was fought in 205 BC between the army of Han, as commanded by Han Xin, and the Zhao army. The general, Han Xin positioned his army with their backs to the river, meaning his army could not retreat in case of defeat. The Zhao army saw this and thought Han Xin must be an idiot that didn’t know how to manage an army.
However, this was all a part of Han Xin’s strategy - he wanted to make the Zhao army think he was foolish to put them off guard, and keep his soldiers focused on fighting since retreat was not an option. The Zhao army took the bait and came out of their heavily defended camp, only to be slowly but surely cut down by Han Xin’s army.
背水の陣 can really only be used when the strategy was done intentionally. It’s a common mistake, even among Japanese people, to use this phrase when one simply runs out of options or comes at the end of his/her rope. For example, if you have a big project and didn’t start it until a day before it was due, you would not be appropriate to use 背水の陣 here - because it wasn’t part of your plan. However, if you purposefully did not start the project because you know that limited time gives you more energy and focus, then 背水の陣 would be a perfect fit.
Also, we often use this phrase combined with a particle で for 背水の陣で or sometimes with the verb 敷く (to lay), e.g. 背水の陣を 敷く.
I’ll start studying for the exam at the last minute because I tend to slack off when I have too much time.
I started my business by burning my bridge and quitting my job at the company.