Take a look at the Text Wrap palette. You've got five basic settings. From left to right they are:

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1. No wrap. This is the default. Text will flow behind the object. If the frame has a background color, the text won't be visible behind the object.

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2. Bounding Box. Text will flow around the frame that the object is in.

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3. Shape. Text will flow around the edges of the object itself. You can select how InDesign selects the edges under Counter Options in the Text Wrap panel. Detect Edges is InDesign's internal method, where it attempts to find the edges of highest contrast. Another common method of defining object edges for InDesign is with clipping paths made in Photoshop, which InDesign recognizes.

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4. Jump Object. Text will flow above and below the object's frame boundaries, and not to either side at all.
5. Next Column. Text will be forced to the start of the next column or page once it meets the object. This is similar to hitting the "enter" key on your numpad in order to force text to the next column or page, but in this case you're telling the object to function in that capacity.

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Sometimes when you've wrapped text around an object, the text butts up too close to the object for comfort. In these cases, you want to give your object a little breathing room. This is adjusted in the Text Wrap palette similar to how you adjust paragraph spacing. In the image here, I've added 1/8" space around the object, which has pushed the type out from the bounding box. The 1/8" shows as a lighter blue border around the object's frame.
Whether you're new to InDesign, new to layout, or making the switch from Quark to InDesign, knowing how to use Text Wrap is an invaluable tool in your designer's arsenal. I hope this short tutorial has been somewhat enlightening. Feel free to contact me with questions.