What are Transverse/longitudinal effects in lasers?

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Longitudinal means along the direction of the beam. As the beam travels forward with the speed of light, anything in this direction can be written either in the time domain, frequency domain (1/time, equivalent to wave length, ...), or in real space (speed of light * time).

Transverse means perpendicular to the direction of travel. This is a spatial direction related to things such as curvature of the wave front, physical source size, etc.
 
Thanks for the answer! However the question was about what meant by effects, and not what is a transverse and longitudinal directions. Topic still unclear.
 
As was pointed out elsewhere, the longitudinal and transverse properties of the beam are more or less independent from each other. Because of that they each have a set of effects associated with them, i.e. effects that arise because of longitudinal or transverse properties. Speckles, for example, were mentioned as transverse effect.