Omer Counting
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Starting from the evening after the (first) Haggada, we count the days that lead up to the holiday of Shabu'oth. This counting is called "the Counting of the Omer", and is named after an event that took place in ancient times when the Tabernacle, and later the Temple, was still standing. The word Omer is a certain amount of grain (in this case barley) which would be offered to God in the sanctuary as a so-called "moving sacrifice" right after the start of the barley harvesting season. The offering of the 'Omer' was also the beginning of the count, and ever since, up to this day, we count: "Today is the first day from the Omer"; Today is the second day from the Omer", etc. Not only do we count the days, but also the weeks, seven in total, leading up to Shabu'oth. So, from the seventh day on, we count: "Today is the seventh day from the Omer, which is one week"; "Today is the either day from the Omer, which is one week and one day", and so on.
After we have counted seven complete weeks, the Omer counting is complete, and the very next evening is the start of Shabu'oth. The name of the holiday get its name from this count, as it literally means 'Weeks', while the Hebrew week for week literally means 'in seven'.

Before the Omer counting, a blessing is said: 

בָּרוּךְ אַתָּה ה' אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם אֲשֶׁר קִדְּשָׁנוּ בְּמִצוֹתָיו
​וְצִוָּנוּ עַל סְפִירַת הָעֹמֶר

Blessed are You, Lord our God, Master of the Universe, Who sanctified us through His commandments and commanded us concerning the counting of the 'Omer.
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After the counting, it is a wide-spread Sephardi custom to sing Psalm 67.
The seven lines of Psalm 67 are written according to a unique 'Menorah' structure. The middle line (the stem) is longer than the other six, which are flanking it in a mirrored fashion. The number of words of each line (besides the title line) is: 7-6-6-10-6-6-7. Listen and see how this video shows the Hebrew words of the psalm unfold into an actual seven-branched candelabra.
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​Click on the image below to view the video: