You know that 覗く is "to peek," and the kanji 込 means into, so this means to look into or to peer into.

覗き込む is a more active version of 覗く, meaning "to lean in and look closely into something," often with a sense of earnest intent. Depending on the context, it can also convey a feeling of depth, like you're trying to see beyond just the surface of something.

The reading comes from the word 覗く and the kanji 込 put together.