She seems to know something important.

Literal

She [topic-は] some important [thing-こと] [object-を] is-knowing [seems-ようだ].

~ようだ wraps the whole inner clause and converts an assertion into an inference: I'm not stating she knows, I'm reading the signs and concluding it. 重要なこと illustrates how こと works as the abstract-thing nominalizer; it produces 'an important thing' rather than the more concrete 'an important matter' (重要な事柄) or 'important news' (重要な情報). 知っている (the resulting state) is the right form to pair with knowledge — knowing is something you possess, not something you actively do.