Most modern English translations tend to present a fairly simple reading which relates to the daily provision of bread without referring to the difficulty or ambiguity in the wording. Nevertheless, even in the English a certain amount of redundancy can be detected - give us this DAY our DAILY bread.

One line of thought suggests that daily (epiousios) is a way to emphasise that we should restrict our prayer to one day's worth of bread and trust God for tomorrow. During the Exodus, the Israelites were required to collect only enough manna for their daily needs.

Against this reading is the argument the the closest word to epiousios is epiousa. Epiousa means 'the next day'. Jerome (and others) understood this as referring to future (eschatological) bread - see New Day's Bread. Nevertheless, if we are to keep with the more mundane reading referring to material bread, it can simply instruct us to pray for tomorrow's bread. This does create a rather strange petition ('Give us today tomorrow's bread'). It has been suggested (although, in my view not very convincingly) that this refers to the Jewish day beginning at sunset, so that tomorrow is in fact part of that day.  

Origen was one of the first people to argue that Matthew and Luke made this word up because of the clause's inherent clumsiness. We have only three ancient versions; Matthew, Luke and Didache (a Christian instructional document written shortly after the Gospels). These are set out in synopsis below. It can be seen that the Didache follows Matthew's wording. However, Luke does appear to attempt to circumvent the awkwardness of Matthew's version by emphasising the continuing daily request.