开眼 is a separable verb (离合词) meaning to broaden one's horizons or to see something impressive for the first time. It often carries a tone of admiration or surprise — like when you encounter something that 'opens your eyes'. The verb 开 and the noun 眼 can be split when inserting a measure word (e.g. 开一次眼 'get an eye-opening experience once') or with the complement 了 (e.g. 开了眼 'had an eye-opening experience'). The most common usage is as an indivisible unit in phrases like 大开眼界 (greatly broaden one's horizons), but 开眼 alone is also productive.