Simplifying a fraction means reducing it to lowest terms — dividing the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. The fraction 24/36 and the fraction 2/3 represent exactly the same value, but 2/3 is the form you want for answers, comparisons, and further arithmetic. Simplified fractions are easier to compare (is 4/6 or 5/8 bigger? reduce to 2/3 vs 5/8 and the answer is clearer), easier to add (common denominators come from reduced forms), and are what teachers and textbooks expect as final answers.
The workhorse for finding the GCD is the Euclidean algorithm: divide the larger number by the smaller, take the remainder, and repeat with the divisor and remainder until the remainder is zero — the last nonzero divisor is the GCD. For 48 and 18: 48 / 18 = 2 remainder 12; 18 / 12 = 1 remainder 6; 12 / 6 = 2 remainder 0, so the GCD is 6. For small numbers, listing factors works fine too: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, and of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 — the greatest shared factor is 12.
Two finishing details. First, the sign convention: keep any negative sign in the numerator (write -3/4, not 3/-4). Second, improper fractions simplify the same way — 45/12 reduces by GCD 3 to 15/4, which you may then write as the mixed number 3 3/4. Simplifying does not change a fraction's value; it only changes its clothes.