A birthday is the date on which a person was born. It is customary in many cultures to celebrate the anniversary of one's birthday in some way, for example by having a birthday party with friends. It is also customary to treat someone especially nice and generally accede to their wishes on their birthday.
In most English-speaking countries it is traditional to sing the song "Happy Birthday" to the honored person celebrating their birthday. This happens traditionally at a birthday party while someone brings a birthday cake into the room, which is often darkened. The birthday cake is traditionally a highly decorated cake, and is typically covered with lit candles when presented; the number of candles equals the age of the person. The person whose birthday it is will make a silent wish and then blow out the candles. If done in one breath, the wish is supposed to come true. Another superstition associated with birthday wishes is that if you reveal your wish, it won't come true.
The singing of the song also often happens at a restaurant when one gets taken out for their birthday. The server or servers in the restaurant may lead the singing of the song while dessert is delivered to the table (which may or may not be a piece of cake, and may or may not be complimentary). The dessert may feature a sparkler instead of a candle. Other customers at the restaurant usually join in for the singing of the song. At some restaurants the servers may perform special, untraditional birthday songs and dances.
For special birthdays and for when the number of candles might be considered a firehazard, special candles might be substituted for the many individual candles. These candles are in the shape of a numeral; for example on one's 5th birthday there may be only one candle on the cake in the shape of the numeral 5, and on one's 50th birthday there may be only one candle on the cake in the shape of the numeral 50.
People often get (and give!) gifts on their birthday.
There is also a tradition of surprise party. This leads to issues where people feel bad ignored because it appears their birthday has been forgotten when actually it hasn't been mentioned because a surprise party has been planned and, conversely, where people don't mention that nothing is planned for their birthday because they expect a surprise party.
Astrological signs typically depend on one's birthday, or even the specific time of birth.
Notable birthdays can include:
When the most significant digit changes, for example one's 1st, 10th, 20th, 50th, or 100th birthdays.
In most legal systems, one becomes a legal adult on a particular birthday, and at different ages gain different rights and responsibilities -- voting, certain drug use (e.g. alcohol, tobacco), eligibility for military draft, etc.
Most cultures have one or more coming of age birthdays:
Many girls in the USA have "sweet sixteen" birthday parties.
In many countries it is traditional when it becomes legal for you to drink for your older friends to drag you out to bars and get you rip-roaring drunk.