What is the ideal boundary of a Riemann surface?
I came across this in 'A Primer on Riemann Surfaces' by Beardon. On pg.152 it is stated that "a compact surface has no ideal boundary, a parabolic surface has a 'small' ideal boundary, and a hyperbolic surface has a 'large' ideal boundary."
I've tried to find a clear definition online for what the ideal boundary is in this context but to no avail.
I'm also not sure how this relates to the boundary points of Riemann surfaces. For example, the unit disc (or upper-half plane) has infinitely many boundary points, so this seems to match up to the 'large' ideal boundary property. However, I can't make similar deductions for $\mathbb{C}$ or the Riemann sphere. Indeed, I'm not even sure if this is the correct way to view it.