… well, almost. Things are a bit more complicated in practice, and objects can be divided into one of three types, depending on how they react to external fields.
In paramagnetic materials (platinum and aluminum are two examples), the dipoles try to align with the external field as described above. However, it is difficult for dipoles to stay aligned, because the jiggling of the atoms due to thermal noise constantly knock the dipoles out of alignment. Thus, paramagnets are only weakly attracted to bar magnets; so weakly that the effect is usually unnoticeable. (Hold a ball of aluminum foil next to a refrigerator magnet and see if you can feel the attractive force between them. If you can, you have supersensitive fingers and should probably consider a career fighting crime.)
In ferromagnetic materials (such as iron, cobalt, or nickel), dipoles are influenced by their neighbors, and will tend to point in the same direction nearby dipoles point. Before a ferromagnetic material is exposed to any magnetic fields, its dipoles form neighborhoods called domains, in which all point in the same direction. When thermal noise knocks one of the dipoles out of alignment, its neighbors quickly set it right again.
When a ferromagnet is placed in a magnetic field, the domains which point in the same direction as the field will tend to steal dipoles from bordering domains that point in the wrong direction. The material becomes highly magnetized, and the attraction between a ferromagnetic material and a bar magnet is very apparent. This is the feature of magnetism which is most recognizable in everyday life. The magnetized ferromagnet has itself become a magnet, and can magnetize other ferromagnets in turn: so for example a whole chain of paper clips can be suspended from a single magnet.
This magnetization is usually temporary; when the external field is removed, the dipoles return to their original domains. However, under certain conditions the domains can become reorganized, and a ferromagnet can be permanently magnetized. For example, striking an iron bar with a hammer while in a magnetic field can magnetize it. Another method is to heat the material above its Curie temperature, at which point the thermal noise overwhelms the connections between dipoles and the domains vanish. If you then cool the ferromagnet, new domains will form which are aligned with the external field.
Diamagnets are strange. When you place a diamagnetic material in a magnetic field, the dipoles inside effectively align against the magnetic field. The explanation for this phenomenon will have to wait until TBD , but the result is that diamagnets are repelled by bar magnets, not attracted.
Water, copper, and wood are all weakly diamagnetic; the effect is only noticeable for strong fields or with delicate equipment. Superconductors, however, are strongly diamagnetic; "maglev trains" operate by using the repulsive force between superconductors and magnets to make the train levitate slightly above the tracks: not enough to be noticeable, but enough to greatly reduce friction.The toy animation below may make the behavior of the three types of materials clearer. (And it's just fun to play with.)