A partial circumcision can mean different things to different doctors. To some this means just removing the tip, with the rigid band. To some, it means a complete circumcision, just a loose one. So you need to be
very careful about this. It sounds like your doctor is recommending removing just the very tip of your foreskin. This is the rigid band, which causes the foreskin to pucker at the tip, when not retracted. It also tends to cause a narrowed area of the foreskin behind the glans, when retracted. Doctors tend to worry way too much about the rigid band causing complications, like paraphimosis. If you are able to keep your foreskin retracted comfortably, then you are not at risk of paraphimosis, and don't need a circumcision, partial or otherwise. Also, the rigid band is a very sensitive area, and can provide lots of pleasure. So you might miss it if it was removed. And, like Kylar said, it might help with locking the foreskin back behind the glans. Personally, this worked for me only in the beginning, but doesn't anymore, because my rigid band has stretched out enough that it doesn't work like that anymore. Possible benefits of losing the rigid band are a shorter foreskin, if you like that, and it might help it selfretract upon erection, because the rigid band wouldn't pucker at the tip without it. Only you can decide what's good for you, but I recommend extreme caution.
Here is a link to a pick of a very conservative partial circ.
https://commons.wikimedia.org/wiki/File:Foreskin_of_Circumcised_Penis.jpegHere is a link to a less conservative partial circ.
https://www.bloggang.com/viewblog.php?id=thaicirc20&date=23-12-2006&group=8&gblog=2