Pe̍h-ōe-jī is a way of writing words in the Hokkien language using letters from the Roman alphabet (like A, B, C, etc.). It's like writing in English, but with different letters for different sounds.
For example, instead of writing "hello" as "h-e-l-l-o," in Pe̍h-ōe-jī it would be written as "ho-ló." Each letter represents a different sound in the Hokkien language.
Pe̍h-ōe-jī was created a long time ago to help people who spoke Hokkien but didn't know how to read and write Chinese characters. It's still used today in places where Hokkien is spoken, like Taiwan and parts of China.