When things vary, they aren't the same, or they don't stay the same: they're different from each other. They change from time to time, and they're different from one situation to another.
For example, your mood can vary throughout the day: you might be happy in the morning, angry in the afternoon, then calm and relaxed at dinnertime. Your mood varies because various things happen throughout the day.
And when you have various things, you can call them a variety. A variety is a group of many different kinds of things. For example, a good menu offers a variety of foods: lots of different foods for you to pick from.
And I bet you have a variety of friends: quiet friends and loud friends; silly friends and serious friends; friends of different sizes and shapes; and friends who like all kinds of different sports and activities.