Upgrading is using skill points to improve an aspect of a character. This can include things like stats, attacks, and more. You can normally upgrade a character to 15/15/15, unless you have the 50/50/50 gamepass. Some characters (including Announcio and Punk Knight) have upgrades that do nothing. Certain characters gain special abilities/traits when upgraded to 15/15/15 or 50/50/50. You can't upgade secret characters (Indicated by the orange surrounding) unless you have the gamepass allowing you to upgrade secret characters.
Here is a step-by-step picture guide to show you how.
(1. To upgrade you must first buy skill points (SP), or earn them by leveling up.
2. Once you have SP click the "Upgrade" tab under the "Shop" tab.
After you do that you then select a character which you want to upgrade.Any characters with an orange box around them are unable to be upgraded unless you have the pass.
(3. Now select which part of the character you wish to upgrade.
(15 is the upgrade cap unless you have the 50 skill cap gamepass)