DNS stands for domain name system. It is the address book of the internet. Your domain is a name people can remember. The servers that actually hold your website and your email have numbers. DNS is the lookup that turns one into the other, every time somebody visits.
The records you will hear about
An A record points your domain at the numeric address of a server. A CNAME record points one name at another name, which is how most modern hosting is connected. An MX record says which server handles your email, and it is entirely separate from the website.
A TXT record holds plain text, used for things like proving to Google that you own the domain, and for the SPF and DMARC settings that stop other people sending email as you.
The mistake that costs people their email
Website and email are two different services on the same domain. When a new designer sets up hosting, the usual instruction is to point the domain at the new server. If someone does that by wiping the existing records and starting fresh, the MX records go with them.
The website comes up looking perfect and the email stops dead. It is often hours before anyone notices, and the messages sent in the meantime are usually gone.
A worked example
A builder moves his site to a new host on a Friday afternoon. The A record is changed, the site goes live, everyone is happy. The MX records were removed in the same edit.
He finds out on Monday when a customer asks why nobody replied to the quote request they sent on Saturday. Putting the MX records back takes ten minutes. Getting the weekend enquiries back is not possible.