What is ideal with example?

For example, the set of integers (ℤ) forms a ring with ordinary addition and multiplication. The set 3ℤ formed by multiplying each integer by 3 forms an ideal, and the quotient ring ℤ/3ℤ has only three elements: 0 + 3ℤ = 3ℤ = {0, ±3, ±6, ±9,…}