Simple Definition:

A nucleus is the central part of an atom that contains protons and neutrons [particles that make up an atom’s structure]. It is responsible for maintaining the stability of an atom by holding its particles together.

For example, the nucleus of a hydrogen atom has only one proton, while the nucleus of a helium atom has two protons and two neutrons.

Very Simple Definition:

The nucleus is the center of an atom that holds everything together. It’s like the skeleton of the atom.

For example, an atom of iron has a nucleus, surrounded by electrons.