The world contains many individual things (objects or particulars), both physical and abstract, and what these things have in common with each other are called universals or properties. Metaphysicians are interested in the nature of objects and their properties, and the relationship between the two (see the sections on Realism and Nominalism).
The problem of universals arises when people start to consider in what sense it is possible for a property to exist in more than one place at the same time (e.g. a red car and a red rose). It seems clear that there are many red things, for example, but is there an existing property of 'redness'? And if there is such a thing as 'redness', what kind of thing is it? See the section on Realism for a further discussion of this.
Any object or entity is the sum of its parts (see Holism). The identity of an entity composed of other entities can be explained by reference to the identity of the building blocks, and how they are interacting. A house can be explained by reference to the wood, metal, and glass that are combined in that particular way to form the house; or it could be explained in terms of the atoms that form it (see the sections on Atomism and Reductionism).