There is some sense in which there are wholes that are more - or other - than the sum of their parts, just as a building is more or other than the collection of the bricks from which it is built, but it is difficult to spell this out in clear and rational detail, and when this is to some extent succesfully done this will tend to be formal and mathematical (see e.g. Simon, Woodger, or Souriau).

In such rational accounts, what makes a whole, such as the house from its stones, beams, tiles etc. are specific relations between the parts, that make it cohere into the structure that forms the whole.

This one can illustrate even in geometry: What makes a triangle is not just some gathering of three straight lines, but three straight lines such that the endpoints of each are connected to an endpoint of each.

Apart from more or less mathematical theories of wholes and systems (and indeed including some of these: think of some expositions of "systems theory"), holism is a modern cant term, that is used to give status and an appearance of depth to what are in fact usually deeply nonsensical but quite possibly highly remunerative theories, often in the social sciences or para-medicine.

In brief, when you read 'holistic' or 'holism' beware, especially if there is no mathematics, or such mathematics as there is is beyond you.