Understanding triangulable topological spaces

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Let $X$ be a topological space. If there exists a simplicial complex $K$ and a homeomorphism $f:|K| \rightarrow X, X$ is said to be triangulable and the pair $(K, f)$ is called a triangulation of $X$.

Topology, Geometry and Physics- Nakhara, 2nd ed,pg-101

I have some doubts on the following definition:

  1. How does one actually 'think' of triangulating topological spaces? Is there some visual intuition for it?
  2. I am confused on how the homomorphism is done. I suppose it maybe mainly because I don't understand the topology of simplical complexes.