If your server has cracked mode enabled in the options page, skins are usually not working.
You can try to restore the skins with a plugin like SkinsRestorer: https://exaroton.com/addons/a/spigot/2124
This article explains how to install plugins.
The other option is to disable the cracked setting here: https://exaroton.com/options/ (if all players have a premium Minecraft account).