The Internet depends on a system of servers that convert human-friendly names like "ReverseMX.com" into an Internet address (known as an "IP address"). When someone types a website address (called a "URL") into their browser, their computer must first retrieve a domain name record so it knows which IP address to send the request to.
A similar process happens when you send an email, except that email servers ask for a special kind of record called an "MX Record" ("MX" stands for "Mail eXchanger"). That record provides the IP address (or addresses) of a server that can receive messages for a certain domain name.
SPF stands for "Sender Policy Framework" which describes an optional mechanism mail servers can use to verify whether to trust the source of an email message. Participating mail servers for a given domain name publish a special type of domain name record that lists which servers are authorized to send mail for a domain name.
For example, your email server receives a message that claims to be from PayPal.com about your account. Your email server first checks the source Internet address (or IP address) the mail is coming from, and then retrieves the SPF records for PayPal.com. If the IP address is not listed in the SPF records for PayPal.com (or in one of the domains those records refer to), your email server may delete the message or mark it as spam to warn you about the mis-match.
Unlike MX records, SPF records are not required to make email work properly, and not all domain names publish them. Most mail servers will still accept email for domains that do not publish SPF records, but some more zealous servers will not. The best practice is to always publish accurate SPF records for your domain names to ensure the best likelihood of delivery.