A field is an algebraic structure with certain properties.
It is a set of mathematical objects on which are defined two binary operations, namely addition and multiplication.
The operations are commutative (e.g. x*y = y*x) and associative (e.g. (x+y)+z = x+(y+z)) and have identity elements (e.g. 0 for addition and 1 for multiplication).
They have inverse elements (e.g. x and -x for addition; x and 1/x for multiplication). Multiplication is distributive over addition (i.e. x*(y+z) = x*y + x*z).
A finite field is a set with these properties, but it only has a finite number of elements.
Hope this helps!