This is the distance between strings. In general, harps start with the narrowest space between the strings at the treble end (shortest) and gradually get wider as they descend to the bass. This is due to the tendency of the longer (and thicker) strings to move back and forth more when you pluck them. If the strings are too close together they could bump into each other. It also allows the fingers to get between the strings without the fingernails buzzing against a neighboring string. In general, the wider the spacing, the more flesh can go between the string. This also affects the possible hand shapes used when playing. Since all the spacings start out fairly narrow at the top, it's primarily in the bass where players will feel the most difference.
Classic (Classical/Pedal Harp) - This is the most common string spacing in Europe and the U.S. It is also the widest of the three. It allows for powerful playing on larger harps without the danger of buzzing (remember, the pedal harp evolved to be heard in the middle of a modern symphony orchestra). It also allows for angling the fingerpads into the strings in ways that are more difficult on narrower spacings and which produce a very full tone. It's better for linear, scale-like passages than the Latin/historical spacing. My Butterfly and SweetHarps use this spacing (since there's little difference in the treble range between this and the Celtic spacing).
Celtic (Modified Traditional) - This is a compromise between the classical spacing and the Latin/historical spacing. It starts the same in the treble, but doesn't get as wide as quickly in the bass. This makes it fairly easy for modern players to adapt to and provides many of the benefits of the narrower spacing without sacrificing those of the wider. It emerged during the 1970s when the new wave of Celtic harps began to be built. The current refinement is based on my years playing the Paraguyan harp and my work with several fine old pedal harps. My Gwydion is in this spacing, and my Rhiannon and Conservatory have it as an option.
Latin/Historical - This is the narrowest spacing. It is the spacing of the old Clarsachs and of the modern Latin American harps. It lends itself to octaves, single-handed chords, and forked-finger techniques. It is also the easiest on the hands. Playing a harp with this spacing is like driving a race car. Most commonly played with fingernails. There are more harps, harp players, types of harp, and music for the harp in Latin America than in the rest of the world combined. That means that more people play this spacing than any other.