That indicates that there are 2 voices being played simultaneously. Look a measure 3 - the A# should be left to ring, then the 16th note figure is played on beat 2 leading up to the high D#. The 2 half notes (the A# and high D#) are a single "voice" while the the rests are associated with the voice that has the 16th anf 8th notes. I hope this helps!
14th June, 2017