Spring is a season that affects the world outside of the tropics. Areas beyond the tropics have seasons related to how warm it is. So they have spring, summer, autumn/fall, and winter.
The changes in length of day, and the warmth of the air has a great effect on plants and animals. Most plants do not grow in winter because it is too cold. Some animals hibernate because there is much less plant food in winter and early spring. But as the days become a little longer, those plants that have stored up reserves in bulbs begin to send out shoots and then flower. Snowdrops, crocuses, daffodils and so on, are all bulb flowers.
While this is happening, the deciduous trees are still without leaves. Many trees begin to make flowers before they make leaves. This is called blossoming. Flowers are delicate, and so trees try to flower when most or all of the frosts are past. The closer you are to the tropics, the earlier frosts stop, so spring starts earlier near the tropics. If you are closer to the poles, or in a mountain area, spring will be that much later.
Most deciduous trees put on leaves towards the middle or end of spring. By this time the bulb plants have flowered, set seed and died back. The last trees have their leaves by the time summer begins.