They are very similar, of course. And sometimes, they can be used interchangeably. However, there is a slight difference. "walk to" means to go somewhere, but it doesn't necessarily reference a specific spot and it doesn't say anything about what you will do when you get there. I will walk to school. (But then I will walk to my first classroom.) "walk up to" has a feeling of going to a specific spot for a defined purpose and stopping. Walk up to that man in the park. (He will show you where to find the statue.)

Mojave's explanation is pretty good, except that I would go one step further, and say that you 'walk up to' an object (including a person). You walk to the park. You walk up to a man, and ask him where the statue is. You walk to the centre of the park. You walk up to the statue.

Up simply means reach. walk to means walking toward walk up to means walk to reach the destination Example: Walk up to that man in the park. (He will show you where to find the statue.) Here, it means you walk to reach that man ( He will show you where to find the statute. ) Example: I walk to school. Here it means you are walking toward the destination. (school)