You're right to want to understand them. Let me offer you the simplest explanation of all spells.
The basis of magic, the very basis, is the shifting and changing of energy. As energy changes and moves it causes these specific reactions. Magic is in everything, as everything takes energy.
Now what spells are, are simply tools. Tools to direct energy, to give it a heading, and to act as a catalyst for change.
Spells are simply actions, words, anything that assists in manipulating energy to cause the desired effects.
Spells come in many forms, complex rituals, simple chants, movements using objects like the athame; it's all for directing energy.