A tensor is a generalization of the notion of scalars and vectors. A tensor of rank 0 is a scalar (it has $3^0$ compenent), while a tensor of rank 1 is a vector (which has $3^1$ components). In general, a tensor of rank $n$ has $3^n$ components.
See http://www.google.co.in/url?sa=t&rct=j&q=tensors%20nasa&source=web&cd=1&ved=0CFQQFjAA&url=http%3A%2F%2Fwww.grc.nasa.gov%2FWWW%2Fk-12%2FNumbers%2FMath%2Fdocuments%2FTensors_TM2002211716.pdf&ei=fyUBUIKFKI_NrQe9stn1BQ&usg=AFQjCNHNTtYW7SS-_n9DHzPmbpKdoNehTA&cad=rjahttp://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf for a nice introduction.