In general, catalytic cycles can be divided into 3 stages:
# Coordination of the starting material(s)
# Catalytic transformation of the starting material(s) to the product(s)
# Displacement of the product(s) to regain the catalyst (or pre-catalyst)  
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Traditionally the focus of catalytic research has been on the reaction taking place in the second stage, however there will be energy changes associated with the beginning and end steps due to their effect on the coordination sphere and geometry of the complex, as well as its oxidation number in cases of oxidative addition and reductive elimination. When these energy changes are large they can dictate the turn-over rate of the catalyst and hence its effectiveness.
Hemilabile ligands reduce the activation energy of these changes by readily undergoing partial and reversible displacement from the metal centre. Hence a co-ordinately saturated hemilabile complex will readily reorganise to allow the coordination of reagents but will also promote the ejection of products due to re-coordination of the labile section of the ligand. The low energy barrier between the fully and hemi coordinated states results in frequent inverconvertion between the two, which promotes a fast catalytic turn-over rate.
Hemilabile ligands dissociate in one of three main ways; an "on/off" mechanism where they are constantly dissociating and re-associating, a displacement mechanism where they dissociate easily when exposed to a competing substrate, or redox switching where the oxidation state of the ligand is used to tune its affinity for the metal center.