Small or relatively small amounts of the antigen can cause an allergy, when you have IgE antibodies which fit to this antigen. They will then cause a local immune reaction and cause the secretion of histamine.
For the desensitation therapy large amounts of antigen are given (which is not without risk). The mechanism behind this therapy is not completely understood, but there are some good points.
The immunetherapy seems to induce class switching from the IgE antibodies which can trigger allergic reaction to IgG who can not do this. Furthermore the IgG will mark the antigen for uptake and degradation by the mast cells.
This seems to be induced by a shift from a Th2 immune response over to a Th1 response. This also leads to the production of a different set of cytokines which are anti-inflammatory (IL-10 for example) and the already mentioned different secondary immune response. The immunetherapy reduces the amount of mast cells, basophils and eosinophils which are recruited into skin, nose, eye and the bronchial mucosa. These cell usually support the reaction to allergens in this tissues after the exposure.
See these papers for more information: