Real numbers are basically all the numbers you could think of if somebody told you to think of a number. Real numbers are based on the concept on the number line: the positive numbers sitting to the right of zero, and the negative numbers sitting to the left of zero. Any number that can be plotted on this number line is a real number. The numbers 27, -198.3, 0, 32/9 and 5 billion are all real numbers. Strangely enough, numbers such as √2 (the square root of 2, the value of which is 1.14142...) and π (3.1415...) can be plotted on a number line as well, even though they are nonterminating decimal numbers. So, even though the number after the decimal never ends, they can still be plotted on the number line.
Real numbers can also be described as all the numbers that are either rational or irrational. Rational numbers are numbers that can be written as a fraction, which includes whole numbers, all of which can be written as a fraction: 3/8, 5/1, 9/10, etc. Decimals can be rational as well — they're just numbers that have either terminating or repeating decimals. So, 8.372 is a terminating decimal and 5.2222222... is a repeating decimal. These are rational numbers, which are also real numbers. Irrational numbers are also real numbers: those are decimals that are nonterminating like π and √2.
In contrast, an imaginary number is the value of the square root of a negative number. You may remember this special little math rule, but there is no number that, when squared, will produce a negative number. But that doesn't stop mathematicians from doing it, as long as they admit the result is imaginary. Infinity is also an imaginary number.
