In the context of airborne LiDAR and forestry, local maxima algorithms such as the one described in Popescu et al. (2002) were designed to identify and extract individual trees in the forest.
Given some digital surface model (usually, a canopy height model), the local maxima algorithm will search for the highest point inside a window of search, and it will label that point as the top of a single tree (i.e., its total height). A window search's width can be fixed or variable.
For example, the command line
CanopyMaxima from Fusion/LTK offers the local maxima algorithm from Kini and Popescu (2004), which window size is a function of height:
width of window search = A + B * ht + C * ht² + D * ht³
where, ht is the height at the center of the window search. The higher is a tree/point, the lesser are the chances to detect a neighbouring tree, because the window's range will be larger.
A variable window search will make sense when the forest is uneven in age and its horizontal structure is not known. A fixed window search will make more sense for even-aged plantations (depending on its tree spacing; for example: higher than 12 m² per tree and with trees regularly spaced).
Generally, such algorithms are more suitable to identify the highest trees and fail to detect the ones in the middle and in the understory layers of the forest. It is considered a best practice to validate such algorithms with measured field data, or high resolution satellite imagery, before applying them operationally.
Specifically about the tools available in LiDAR analyst for tree segmentation, there is this tutorial available on Scribd, but it is not free.
Kini, A.U.; Popescu, S.C. 2004. TreeVaw: A versatile tool for analyzing forest canopy
Lidar data – a preview with an eye towards future. Kansas City, MO: SPRS Images to
Decision: Remote Sensing Foundation for GIS Applications.
Popescu, S.C., R.H. Wynne, and R.F. Nelson, 2002. Estimating plot-level tree heights
with lidar: local filtering with a canopy-height based variable window size, Computers
and Electronics in Agriculture, 37(1-3):71-95