What is the function of dendritic cell in immunity?
Dendritic cells are so called professional antigen-presenting cells (APCs) as pointed out by Sleepes in comment section. They express both MHC-I and MHC-II receptors on their cell surface on which they present small peptides. These small peptides come from digested proteins of their own (MHC-I) or antigens that were phagocited or taken up by receptor mediated endocytosis (MHC-II). They also express costimulatory molecules necessary for the activation of T-cells (eg. CD80/CD86).


source: http://journals.cambridge.org/fulltext_content/ERM/ERM2_09/S1462399400002143sup004.htm

As you can see in image above, activation of a T-cell requires two distinct signals: the recognition of an antigen and a co-stimulatory signal.


source: http://www.mhhe.com/biosci/ap/dynamichuman2/content/gifs/0158.gif

After activation T-cells undergo rapid division and diversification.

Details of T-cell activation by dendritic cells can be found in this article for example:
Immunol Cell Biol. 1997 Jun;75(3):223-30.
The role of dendritic cells in T cell activation.
Ni K1, O'Neill HC.