If you want to have your Adenium growing many blooms then you need to trim its stems and let the stems grow more stems and the trimming continues with time, your Adenium will have more branches. With feeding of fertilizers on a regular basis (Adeniums need heavy & regular feeding of fertilizer in order to bloom), blooms will appear on these branches. The illustrations below (courtesy of the Adenium Yahoo Group) shows how an Adenium plant should be trimmed.
Another reason to trim the stems is when the stems have grown too long (just like the photo below). You may have seen many of such Adenium. Usually Adenium that looks nice are those with thick stem. In order to get those thick stems, you need to trim the long ones. Thus nutrients will be provided to the remaining stems and over time, they will thicken up ~ just like the Adenium in the garden of my friend, Rox.
The next 3 photos show the Adenium that I have newly trimmed.