If you plan to change web hosts in the future and don’t want an interruption to your service. You should consider using a third party DNS service provider. If you have no plans to change web hosts in the future or having a few days of downtime won’t impact you then using your web hosts DNS servers should be fine.
When you signup for web hosting your web hosting provider you will provide you with their nameservers. You would need to login to your domain registrar and update the nameservers for your domain to point to your web hosts. When you decide to change web hosting providers this can become a source for downtime when transitioning from one DNS server to a another.
When you use a third party DNS service you can set the values and change the IP that your website points without causing a lot of interruption to your websites uptime. If the website you are hosting is a personal site or blog then using your web hosts nameservers should be fine. If the website you are running is critical and needs to be available 24/7 then you should go with a third party DNS service.