For young babies, a firm mattress is important to prevent SIDS or suffocation. However, once a child is a year old, the danger of SIDS lessens, and your toddler will outgrow his crib and transition to a bigger bed. When this happens, he might need a new mattress, which doesn't necessarily have to be as firm as a crib mattress.
A toddler mattress should be comfortable enough to help your child sleep. If she has had difficulty sleeping well on a crib mattress, a slightly softer mattress may help her sleep better.
You can buy a mattress that's specifically designed for a toddler bed, bigger than a crib but smaller than a twin. However, many cribs also transition into toddler beds, in which case you can continue using a crib-sized mattress. In addition, some crib mattress have a "dual firmness" feature, in which one side is firmer for a baby's use, while the other side is slightly softer and more comfortable for a toddler.
You should wait until your baby is at least a year old to switch to a toddler mattress. Most parents wait until their child tries to climb out of the crib, at which point the crib is no longer safe, which for most children happens when they are older than 18 months. You can also wait until your child begins potty training, at which point you will want him to be able to get out of bed to go to the bathroom in the middle of the night.
The best toddler mattress should ventilate well and meet all safety standards, including flammability. In addition, it's best if the mattress is waterproof, since most toddler mattresses will suffer occasional diaper leaks or potty training accidents.
If you are using a convertible crib mattress, it should be at least 27-1/4 inches wide, 51-5/8 inches long and 6 inches thick. When you put it in the toddler bed, there should be no gaps around the edges; you shouldn't be able to fit more than two fingers between the mattress and the bed. Toddler mattresses vary in size, so test the mattress in the bed to make sure they fit each other before you buy.