That can be divided by 60 into degrees, which are 0.0174532925199 radians
Those can be divided by 60 into minutes, which are 0.0002908882086 radians
Those can be divided by 60 into seconds, which are 0.00000484813681109 radians
Those can be divided by 60 into thirds, which are 8.08022801849E−8 radians
I think going any further is likely to be meaningless in a modern context, but fourths and fifths were used in the past.
For an arcsec, the square sin is ~85e-9. At the distance of the Moon, that means the signal occupies ~400km^2. At the distance of the Sun, ~5 billions of km^2 (5Mm^2).
The signal intensity is inversely proportional to that area.
One arcminute is about the resolution of the human eye. That is, if two points are less than 1 arcminute apart on the your field of view, they appear as one point.
The moon is 30 arc minutes (1/2 degree) on your field of view, that's why one can see the details of the surface with the naked eye.
18 arcseconds is about the size of Saturn (without the rings) as seen from the earth. It means it is just precise enough to shoot through the rings of Saturn. You can't see this without magnification, like with a small telescope or a good pair of binoculars.