I assume that you are referring to low frequency (or static) magnetic fields. Note that this answer may not apply to high frequency fields. The answer is more complex if the fields are changing. If you are interested in quickly changing fields, you should post a new question specifically about that.
Because ';magnetic monopoles'; don't exist, there is no way to block a magnetic field directly like you can with an electric field. However, you can surround an object with a material of much higher ';magnetic permeability'; and a large proportion of the magnetic field will travel through that surrounding material instead of through the object it surrounds.
For example, a box with sides made of iron will assist in ';shielding'; the contents from a magnetic field because surrounding field lines will have a tendency to bunch up around the iron box rather than going through the air inside the box.
You may want to check out the third source below, on ';Mu-metal,'; which is a special alloy with a very high magnetic permeability. To quote it, ';The high permeability makes mu-metal very effective at screening static or low-frequency magnetic fields, which cannot be attenuated by other methods.';
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