A set having definite number of elements is called finite set. In other words, we can say that the number of elements of a set is defined called finite set.
A set which is not having definite number of elements is called infinite set.
Example:

A = {1, 2, 3, 4, 5, ……………., 100}

B = {1, 2, 3, 4, 5, …………………….}
Set A is finite set and set B is infinite set.
Cardinal Number: The number of element in a finite set is called cardinal numbers of a set. Let A = {a, e, i, o, u} Then n(A) = 5 
Some more examples for your reference are given below:

A = {x : x is a point on a straight line}

B = {x : x is a month in a year}

C = {x : x is a student of class XI in a school}

D = {x : x is a line parallel to x – axis}

E = {x : x is a prime number less than 99}

F = {x : x is a set of circle passing through origin}

G = {x : x is an integer}

H = {x : x is a letter of English alphabet}
Here B, C, E and H are finite sets. But A, D, F and G are infinite sets.