To begin is to start. When it begins to snow, every flake looks pretty, drifting gently down from the dark sky.
When you begin something, you go ahead with its first part or stage — you can begin the day with a good attitude, or begin a very long book over and over again, always falling asleep before you get to chapter two. You also might begin a journey by lacing up your hiking boots. Things also begin when they have a specific element as a first part, as when a word begins with the letter T.