SPF stands for Sender Policy Framework. It is a DNS TXT record that specifies which IP addresses and/or hostnames are allowed to send emails from a specific domain. SPF records are used to prevent spammers from sending messages with forged From addresses at that domain.
A
Stands for including every A-Tag inside your dns, also subdomains
MX
Stands for including every MX-Tag inside your dns
~all
Stands for softfail, which means that mails outside an included mailserver will be delivered into spam
-all
Stands for hardfail, which means that mails outside an included mailserver will not be delivered