From Bulbapedia, the community-driven Pokémon encyclopedia.
The aging of characters in the anime has been a subject of common fan debate, since it is not addressed by the anime itself. The passage of time is clear, but characters show small, if any, signs of aging, despite openly saying that years have passed. The writers and character designs seem to ignore the issue of aging, usually so the viewers of the show feel closer to the protagonists. It is easier for a child to relate to a ten year old rather than a twenty year old.
One common theory is that, like in many cartoons, the characters never age and are trapped at the age of their first appearance. However, this seems strange since the passage of time is pointed out every once in a while without the mention of any character's birthday. It is even more questionable that the anime has directly pointed out years of time passing. One of the most common supports for this theory is that Ash and May are supposedly the same age when May begins her journey, even though Ash has traveled through two regions and competed in three leagues before she received her first Pokémon. This is also the case when Dawn starts her journey as she is the same age as Ash, even though he has been through three leagues by this time, as well as traveling through Kanto twice.
This is easier to believe in the Japanese version, where all characters have retained mostly the same voice. However, in the English dub, many characters have had their voice change over time, especially Ash, whose voice has become noticeably deeper over the seasons. Brock and his family are often used as evidence towards this idea as Brock should always be five years older than whatever age Ash is assumed to be and his youngest siblings barely look any older between Showdown in Pewter City and SS025.
Another common theory is that, because only one half-hour episode airs approximately each week, the flow of time in the anime is considerably slower than in real life. This theory is supported by the apparent, though minimal, growth of the characters, as well as the noted marks of time. The common estimate is that three real years translates to one year in the anime. However, this theory still faces the same problems as the Eternal Youth theory.
Another theory is the Honeydew Lifestyle. In the Honeydew Lifestyle theory the label of an age has a different significance in the Pokémon world than in the real world. In their culture, the numerical "age" of a person is not representative of the amount of years which they have lived, but representative of the person's familial status. When a person comes of age and is ready to head out into the world of Pokémon, they are labeled "ten." When a person has children, they are labeled "twenty." When they have grandchildren, "fifty." Other ages may exist but there is not enough evidence to deduce these ages and milestones in one's life. The theory argues that these seemingly young ages for things like having (grand)children are similar to the surprisingly young age at which children come of age. Ash may well have been alive eighteen years, but hadn't earned the position of "ten." Brock's familial role is most accurately described with a half-age, fifteen. He doesn't have children of his own but he takes care of his younger siblings in the absence of his parents.