DNS records explained: A, CNAME, MX and TXT without the jargon
DNS is a phone book. Your domain is the name; the records say where to send people.
A record points a name at an IPv4 address — the numeric address of a server. This is what makes yourdomain.co.uk load your website. AAAA is the same thing for IPv6.
CNAME points one name at another name. You would use it for www pointing at your main domain, or for a service that asks you to point a subdomain at theirs.
MX decides where your email goes. Each MX record carries a priority number; lower numbers are tried first. Without a priority, the record is meaningless, and most providers reject it outright.
TXT holds plain text, and is how you prove things: SPF and DKIM records that stop your email being treated as spam, and the verification strings services ask you to add.
The two mistakes that break sites
A CNAME on the domain itself. You cannot put a CNAME on the bare domain (the "apex"). The apex has to carry other records that a CNAME is not allowed to sit beside, so the result is either rejected or breaks your email. Use an A record there instead.
A CNAME next to other records. A name with a CNAME cannot have anything else. If www is a CNAME, it cannot also have an A record.
Finally: changes are not instant. Every record has a TTL — how long resolvers are allowed to remember the old answer. If you are planning a move, lower the TTL a day in advance and the switch will be far less painful.