Vowels are a,e,i,o,u, everything else is a consonant. Voiced/voiceless, refers to vibration of the vocal chords when making the sound. Pronounce 's' and 'z'. They both have the same mouth movements/shape but with a 'z' you vibrate your vocal chords.
's' is unvoiced, 'z' is voiced
'k' is unvoiced, 'g' is voiced
't' is unvoiced, 'd' is voiced
-note that these letters in Japanese Kana take the unvoiced character and just add the " looking part to change the sound.
窶堋ゥツ ツ−ツ 窶堋ェ
窶堋ウツ ツ−ツ 窶堋エ
窶堋スツ ツ−窶堋セ
I think what the lesson you are refering to is that sometimes vowels are not strongly pronounced (they call it whipered, I guess). "douitashimashita' sounds like 'douitashimashta' Not the missing 'i' near the end.
Similarly, 'desu' sounds like 'des'.
When you speak the words at a normal pace, it makes sense. It really feels odd to pronounce the vowels in those places.
'sumimasen' is fully pronounced, 'm' and 'n' are voiced so there are no vowels between unvoiced consonents.