To come across something means to find it by chance, without looking for it. When you're cleaning your room and come across an old toy you forgot about, you weren't searching for it: it just appeared while you were doing something else. A hiker might come across a beautiful waterfall while exploring a new trail, or a student might come across an interesting fact while researching a different topic entirely.

The phrase also means the impression someone makes on others. When people say “She comes across as friendly,” they mean that's how she seems to others, whether or not that's how she feels inside. A nervous person giving a speech might worry about how they're coming across to the audience. Sometimes someone comes across differently than they intend: a shy person might come across as unfriendly even though they're just nervous about meeting new people.

In both meanings, there's an element of discovery or appearance: you either discover something you weren't expecting, or others discover something about you through the impression you make.