distribute, disseminate, partition, understand
頒 centers on dividing something and giving it out: distributing, disseminating, or partitioning. The 'understand' sense is a less common extension, possibly from the idea of breaking down information to make it clear.
頒 combines 分 (divide) and 頁 (head), suggesting the idea of dividing something among heads or people, i.e., distributing. The exact historical development is uncertain.
Imagine a head (頁) being divided (分) into parts to distribute knowledge or goods. The head splits to disseminate understanding.
For ハン, picture a hand (ハン sounds like 'hand') distributing items: hand -> ハン, and the hand divides and gives out.