Excellent question! The inner core gained most of its heat very soon after the Earth formed about 4.56 billion years ago. There were two main processes that produced the heat to make the core of the earth hot: One was accretion. The earth formed by the collision of millions of smaller bodies of rock (like asteroids and small planets) and dust that stuck together through gravity. When these building blocks came together, gravitational potential energy was released in the form of heat. The other process that released heat was the differentiation (separation) of the earth into the core (which is mostly made up of the elements iron and nickel) and the mantle (which is mostly made up of silicon and oxygen). Right after the earth formed, all of the iron, nickel, oxygen, and silicon (and lots of other elements) were mixed together, but they separated because they were more lower free energy when they separated into a core and a mantle. Chemical processes released heat when they go to lower free energy. These are probably the most important reasons for why the core of the earth is so hot. The core (and the whole solid earth, not the atmosphere) have cooled down steadily since the earth formed.

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The inner core of the Earth is hot because radioactive decay heats the Earth's interior. When the Earth formed, small amounts of uranium got entombed inside of the Earth, and as that uranium decays into lead, it releases energy, and that energy powers all volcanoes and earthquakes that the heat from inside of the Earth causes.

Earth's core is hot for a few reasons. One reason is that there is still residual heat from when the planet first formed. The process called "accretion" is responsible for the formation of planets. In the accretion process, objects collide and stick together, and large amounts of heat are generated.

Another source for the heating of Earth's core is the fact that it is under immense gravitational pressure due to forces exerted by the sun and moon, as well as the fact that the earth is rotating. This pressure helps to keep the core hot.

One other reason the Earth's core is hot is because of nuclear fission/radioactive decay processes that heavy elements in the core undergo. It's like there is a giant nuclear reactor inside of the Earth and these processes generate a lot of heat!