What you are watching here are acoustic harmonics (pay attention to the way they change depending on the sound frequency). The acoustic waves produce vibrations on the table which are proportional to the the intensity pattern.
In a very simple model, a laser can be described as a cavity with an active medium inside. The field pattern measured in a perpendicular plane to the cavity is the so called transverse mode. They depend on the cavity geometry.
Some examples:
They are denoted by TEMplq, where p is the number of radial zero fields, l is the number of angular zero fields and q is the number of longitudinal fields. The TEMoo is usually preferred as it is easier to be focused.
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