The Torah commands (Leviticus 23:15-16) that we count seven weeks, and also that we count 50 days. Thus we count both days and weeks. For example, tonight's count is "18 days, which are 2 weeks and 4 days of the omer".
So why don't we count the 50th day??? It makes sense that we stop counting weeks after the 7 weeks are completed, and so we don't count the 50th day (Shavuot) as "7 weeks and 1 day". But why not just count the number of days without the number of weeks?
This is a real question - I don't know the answer.