From the second day of Pesach until the Holiday of Shabuot, we count 49 days / seven weeks. Every night, when the new Jewish day begins, we pronounce a blessing and proceed to count that specific day and. After the sixth day we count also the weeks. Today, for example, we counted nine days of Omer, which are one week and two days.
The counting of the days of Omer connect between the exodus from Egypt --when we got our physical, political and legal freedom after being slaves of Pharaoh for so many generations-- with the giving of the Torah, or more specifically: the beginning of our pact with God, which conditions, clauses and articles are stipulated in the Torah.
Originally, the days of Omer are meant to be days of happiness, when we count, enthusiastically, every day until our final goal was achieved: to become, out of our own will, the People of God. The days of Omer are compared with a bride and a groom, who having established the date for their wedding, count enthusiastically every day until the wedding night.
For a deeper understanding of the change in the popular vision of the days of Sefirat haOmer see here. http://www.aish.com/tp/i/moha/48943991.html
If one forgets to count the day at night, one could count it during daytime until sunset, but without reciting the blessing for that day.
If one forgets to count one day completely, then he can count during the following days, but without pronouncing the blessing anymore.
For a summary of Minhaguim of Sefirat haOmer, see here: http://rabbibitton.blogspot.com/search/label/Omer%202011
Rabbi Yosef Bitton. YMJC | 130 Steamboat Rd. | Great Neck | NY | 11024