When a DNS TXT exceeds 255 characters, then it must be split into multiple strings.
As defined in [RFC1035] sections 3.3.14 and 3.3, a single text DNS
record (either TXT or SPF RR types) can be composed of more than one
string. If a published record contains multiple strings, then the
record MUST be treated as if those strings are concatenated together
without adding spaces. For example:
IN TXT "v=spf1 .... first" "second string..."
MUST be treated as equivalent to
IN TXT "v=spf1 .... firstsecond string..."
SPF or TXT records containing multiple strings are useful in
constructing records that would exceed the 255-byte maximum length of
a string within a single TXT or SPF RR record.
This article does not go into all the details of flattening. The purpose of flattening a record is to avoid the dreaded 10 DNS lookup limit perm fail error. Every time you include a 3rd party's SPF record, it counts against your 10 lookup limit. Some 3rd party providers even include other records in their own, so these also count against the limit.
Flattening is the process of converting the included SPF entries into a list of IP addresses and then including them in your record. The downside of doing this is that you must monitor the 3rd party records if they change and then update yours accordingly.