Most atoms are composed of three things: protons, neutrons, and electrons. Protons and electrons are electrically charged, while neutrons are not. Like charges repel (so protons repel one another), but unlike charges attract (so protons attract electrons and vice versa). The protons and neutrons make up the atomic nuclei, while electrons orbit outside.
Because protons are repelled from one another, we cannot easily shoot protons at another atomic nuclei. They will bounce back. As a result, there are two obvious ways to hit the heart of another atomic nuclei:
- Make the proton go really, really fast. This is what particle accelerators do.
- Use something that isn't charged, like the neutron. Because neutrons aren't charged they'll approach the nucleus without being repelled. They can then interact and destroy it.
For some nuclei, adding a neutron to it releases energy. It actually releases a lot of energy (by $E = mc^2$). That's what causes the "explosion" and is a guiding principle behind nuclear fission weapons.
If we send the Earth into the Sun, the Sun is not going to explode. See this related question. The explanation is technical, but the bottom line is that not much will happen.