Recursion is a mathematical term for finding the answer to a question, When
a DNS server uses recursion, it sends iterative queries to DNS servers, that
will provide the answer, or refer it to a DNS server that should know the
answer, until it gets its answer.
For example, when you send a query to your DNS, that is does not have the
answer to, (either from its cache or its zones), it starts at the very top
which is the Root, then works its way down until it either gets the answer
it wants or a DNS server answers NXDOMAIN (non-existent domain). All
recursive queries start at the root.

A real world query to use is www.microsoft.com. If your DNS doesn't know the
answer it starts with the Root servers, which don't do recursive lookups and
will give a referral by a delegation saying, "Go ask the .com gTLD servers",
which also can't do recursive lookups and will answer with a referral by
using a delegation to the Microsoft.com DNS servers. When your DNS asks the
microsoft.com DNS servers, they either give the answer by saying here is the
record or by using a delegation tells your DNS where www.microsoft.com 
should be.

Exactly.

Yes, which is why you have to make sure if you disable recursion on the
forwarders tab, that the forwarder you use is highly trusted. Because if it
fails, or even worse, gives you a bad record which is then cached on your
DNS and your DNS will continue to answer with this bad record, until the bad
record's remaining TTL has expired, that is by default on a MS DNS is up to
one day and seven days on BIND.

A good use of this setting is on a Win2k3 DNS, which has support for
conditional forwarders, you can add a conditional forwarder for a Domain
that cannot be found from the root servers. A good example of this is if you
have multiple Active Directory domain trees such as domain.local that
obviously can't be resolved from the root, but doesn't have a zone on your
DNS, you can add a conditional forwarder for domain.local, give it the IPs
for its DNS servers, select the box "Do not use recursion for this domain",
if the domain.local DNS servers become unavailable, your DNS will answer
with "Server fail" instead of asking the root. It is important that if you
use a Conditional forwarder, that the forwarder has authority for the
domain.