Broadly speaking, algebraic geometry is the geometric study of solutions to polynomial equations. To begin with, you would start by working with solutions in affine space $\mathbb{A}_k^n= k^n$, where $k$ is an algebraically closed field (e.g. $\mathbb{C})$. Eventually, it becomes advantageous to add points at infinity by working in projective space $\mathbb{P}^n_k=\mathbb{A}^n_k\cup (\text{hyperplane at }\infty)$. After a while, you may move beyond even this.