See Linear Regression example: house price prediction 1 dimension We want to predict sales price from feet above ground.
\begin{equation} h(x) = \theta_{0} + \theta_{1} x \end{equation}
This makes: h : \mathbb{R} \to \mathbb{R}. and the \theta = \left(\theta_{0}, \theta_{1}\right) are what we call parameters or weights. d dimensions \begin{equation} h(x) = \theta_{0} + \sum_{j=1}^{d}\theta_{j}x_{j} \end{equation} but this is like clumsy, so if we come up with a special feature x_0 = 1, we can just make it the linear model it is:
\begin{equation} h(x) = \theta^{T} x \end{equation}
so note: this is d features but we have d+1 dimensions for the output.