what does roundness tell us about sediment particles?

The sediments rolled too much before settling. The sediments are
aggregates/pebbles/ small stones.
The sediments travelled at the bottom or bed of river/stream/likes.
The sediments are not dust/likes. The latter traveled downstreams by
floating...except for occassional somersaults in their swim, these
dust seldom experience bumps. Lucky guys!
And, the sediments came from far, far away. It takes too much rolling
to lose those angular ears/vertices/kinks.

Or, the sediments are pellets, ball bearings, cannon balls, or the likes.

Bowling balls?

ticbol is correct in that all of those ways can produce roundness in
sediments.  The question I have is are you sure you're looking at
sedimentary structures?  Very similar appearances can occur in
volcanic rock (which is composed mostly of fine glass particles) as a
devitrification (crystalization of an amorphous solid)process.  A
second possibility - Accretionary lapilli,or mudballs, which form from
particles falling through volcanic ash and increasing in size from
buildup of ash.  One last possibility for volcanic round particles is
from vapor phase crystallization, in that after the hot volcanic rock
has settled, volitiles (co2, h20) are vented through the rock
containing ions that crystalize into the vesicles in the rock.  These
sphere like structures are called lythophyses.  And I suppose pele's
tears (small volcanic glass tear shaped pellets formed from
fountaining lava) could also be a possibility.  Keep in mind too that
some of these formations, if harder than surrounding rock, or in the
case of the pele's tears not formed in rock, can become imbedded in
sedimentary material.

    - GeoEIU