A vector has magnitude and direction, so in 3D we describe it by how far it moves in the $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ directions. For example, $3\mathbf{i}-2\mathbf{j}+5\mathbf{k}$ means 3 units in $x$, 2 units in the negative $y$ direction, and 5 units in $z$.