In general, spring is the time when plants begin to grow again and animals start to procreate. There is a lot that happens in spring, and specifics depend on your location.
Spring is the season when a particular part of the Earth is shifting from being angled away from the sun to being angled toward the sun; this occurs between winter and summer respectively. Spring happens at different times of the year depending on where in the world you are. The angle relative to the sun and the general climate of your location determine exactly what happens in spring.
Some of the most common things that happen in spring are seasonal plants starting to bud, such as trees and flowers. The warming air brings hibernating animals back out into the world, most notably insects, such as bees and wasps. Many animals have mating seasons that cycle around spring, so expect to see a lot of new baby animals around this time. In the majority of climates, rainfall increases greatly during the spring, which helps increase plant growth. During spring, animals begin to lose their winter coats through a process called shedding.
There are many cultures that have holidays and celebrations during the spring, such as Easter for Christians and Passover for Jewish people. May Day is also a common celebration during the spring to celebrate rebirth.