There are 6 different types of reactions: Synthesis, Decomposition, Single Replacement, Double Replacement, Neutralization, and Combustion. Each with a different meaning. So here is the six different types of reactions with their own little description.

Synthesis
A synthesis reaction or also known as a direct combination reaction is one of the most common types of chemical reactions. A synthesis reaction consists of two or more chemical elements to combine and create a more complex chemical form.
A + B = AB or 2K(s) + Cl2(g) → 2KCl(s
http://chemistry.about.com/od/chemicalreactions/a/synthesis-reaction.htm

Decomposition
A decomposition reaction or analysis reaction is when a chemical compound is broken into two or more smaller and simpler chemical elements.
AB = A + B or 2 H2O → 2 H2 + O2
http://chemistry.about.com/od/chemicalreactions/a/chemical-decomposition-reaction.htm

Single Replacement
A single replacement or substitution reaction is formed of one lone element and a chemical compound of two elements. The reaction happens when the unpaired element switches spots with one of the elements in the chemical compound.
A + BC = B + AC or Zn + 2 HCl → ZnCl2 + H2
http://chemistry.about.com/od/chemicalreactions/a/single-displacement-reaction.htm

Double Replacement
A double replacement or metathesis reaction consists of two chemical compounds formed of two elements. The reaction is created when one of the elements of each compound switched places to form two completely different compounds.
AB + CD = AD + CB or NaCl(aq) + AgNO3(aq) → NaNO3(aq) + AgCl(s)
http://chemistry.about.com/od/chemicalreactions/a/reactiontypes.htm

Neutralization
Neutralization or also known as water forming reaction is when an acid and base react to produce water and salt.
Acid + Base = Salt + Water or HCl(aq) + NaOH(aq) –> NaCl(aq) + H2O(l)
http://www.academickids.com/encyclopedia/index.php/Neutralisation

Combustion
A combustion reaction produces either light or heat, the most common reaction is fire. The majority of forms of combustion happen when the gas oxygen joins with another substance. For example, when wood burns, oxygen in the air joins with carbon in the wood. Combustion happens when when the substance reaches a temperature called ignition point. At this point, oxygen combines with the substance fast enough to create a flame (ex/ is when producing fire).
http://kids.britannica.com/elementary/article-399410/combustion