I changed the hosting of a website and their email is hosted with another company. There is also an SPF record for that host.
What is the function of that SPF record?
SPF Stands for Sender Policy Framework. What it allows an administrator to do is specify what servers or internet hosts are allowed to send mail originating from that domain. See this article for more information: http://en.wikipedia.org/wiki/Sender_Policy_Framework
Sender Policy Framework. It's a method of using DNS TXT records in order to reduce SPAM mail. The receiving email server needs to read these records.