Eubacteria is just another word for our everyday word bacteria.
the word eubacteria is the old word for our everyday word bacteria. The problem was back in time that every procaryote organism was called a bacteria and there exist another life-form / domain that was different from the eubacteria - the archaebacteria.
The usage of prefix "eu" in words like eubacteria and eukaryotes caused as "true" confusion. When it comes to eukaryotes, it refers to cell's nucleus while in eubacteria, it refers to prokaryotic organisms which do not belonged to archaebacteria or much prefer as your typical, normal bacteria that encountered in everyday life.