Because the cells of a biological organism have to work together to achieve functionality on a greater scale, they are interconnected by special structures on their adjacent surfaces. Most of those junction structures are anchored to the cytoskeleton, thereby connecting the cytoskeletons of adjacent cells with each other, giving tissue its mechanical stability. Depending on the functions that need to be performed in concert with neighboring cells, there are different kinds of intercellular junctions:

Desmosomes are junctions that provide mechanical stability. Under a microscope desmosomes appear as dense areas where membranes of neighbouring cells are very close to each other. The extracellular space between them is filled with a dark, dense mixture of polysaccharides and proteins. There are a number of sub types to this category (hemidesmosomes, adhesion plaques, spot desmosomes, belt desmosomes and others). There are also junctions called adhesion plaques and zona adherens that fulfill similar functions as the desmosomes but have a different structure.
Tight junctions
Also called zona occludens. These are junctions where the outer membranes of two cells have fused together. This reaction is induced and sustained by transmembraneous linker proteins. Tight junctions are primarily found in epithelial cells because they provide a barrier between the intercellular space on "the inside" and the "other side", thereby inhibiting the exchange of matter (e.g. like preventing the escape of water molecules and such).
Gap junctions
Also called Nexus. They are plaque-shaped, communicative junctions where adjacent cells exchange substances. Each one of those protein-based connections features a mutlitude of small channels, called connexons. Gap junctions are essential to intercellular signalling and provide important means for the transportation of metabolistically relevant substances.