「肉入{にくいり}」 （also written as 「肉入{にくい}り」） simply means "***(an amount of) meat contained***". 

The phrase is used to describe dishes that contain ***small*** amounts of meat.  It is not used with obvious meat dishes such as steaks, beef stew, etc.

You will keep encountering the phrase:

>「[Food item] + 入{い}り」

at eateries and grocery stores.

FYI: In case you want to order the dish prepared ***without*** that particular food item, the phrase to use is explained [in this Q&A][1].

[1]: https://japanese.stackexchange.com/questions/18015/ordering-food-difference-between-%e3%81%aa%e3%81%97-and-%e6%8a%9c%e3%81%8d/18018#18018