Odd numbers are integers that cannot be evenly divided by 2. This means that when you divide an odd number by 2, there is always a remainder of 1. Examples of odd numbers include 1, 3, 5, 7, and 9. They are part of the set of whole numbers and are found between even numbers. Odd numbers can be identified by their last digit, which is always one of the following: 1, 3, 5, 7, or 9. They play a significant role in various mathematical concepts and are often used in patterns, sequences, and problem-solving scenarios.