Does it mean to play all the notes at the same time?
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These groups of multiple notes are called chords.
It does in fact mean to play all the notes at the same time.
The notes you pictured appear to be notation for piano. The two staffs pictured are the treble and bass staffs. The notes on the lower staff are played with the left hand and the upper staff notes are played with the right hand.
And yes, all the notes that are vertically stacked including both staffs - are to be played simultaneously. The notes on the top staff form a chord and the note played at the same time is a corresponding bass note.