A tetramer is a protein with four subunits (tetrameric). There are homotetramers (all subunits are identical) such as glutathione S-transferase or single-strand binding protein, dimers of hetero-dimers such as hemoglobin (a dimer of an alpha/beta dimer), and heterotetramers, where each subunit is different.
Subunit interactions in tetramers 
The interactions between subunits forming a tetramer is primarily determined by non covalent interaction. Hydrophobic effects, hydrogen bonds and electrostatic interactions are the primary sources for this binding process between subunits. For homotetrameric proteins such as Sorbitol dehydrogenase (SDH), the structure is believed to have evolved going from a monomeric to a dimeric and finally a tetrameric structure in evolution. The binding process in SDH and many other tetrameric enzymes can be described by the gain in free energy which can be determined from the rate of association and dissociation. The following image shows the assembly of the four subunits (A,B,C and D) in SDH.
Hydrogen bonds between subunits 
Hydrogen bonding networks between subunits has been shown to be important for the stability of the tetrameric quaternary protein structure. For example a study of SDH which used diverse methods such as protein sequence alignments, structural comparisons, energy calculations, gel filtration experiments and enzyme kinetics experiments, could reveal an important hydrogen bonding network which stabilizes the tetrameric quaternary structure in mammalian SDH.
Tetramers in immunology 
In immunology, MHC tetramers can be used to quantify numbers of antigen-specific T cells (especially CD8+ T cells). MHC tetramers are based on recombinant class I molecules that, through the action of bacterial BirA, have been biotinylated. These molecules are folded with the peptide of interest and β2M and tetramerized by a fluorescently labeled streptavidin. (Streptavidin binds to four biotins per molecule.) This tetramer reagent will specifically label T cells that express T cell receptors that are specific for a given peptide-MHC complex. For example, a Kb/FAPGNYPAL tetramer will specifically bind to Sendai virus specific cytotoxic T cell in a C57BL/6 mouse. Antigen specific responses can be measured as CD8+, tetramer+ T cells as a fraction of all CD8+ lymphocytes.
The reason for using a tetramer, as opposed to a single labeled MHC class I molecule is that the tetrahedral tetramers can bind to three TCRs at once, allowing specific binding in spite of the low (10-6 molar) affinity of the typical class I-peptide-TCR interaction. MHC class II tetramers can also be made although these are more difficult to work with practically.