I have a different perspective on Point-To-Point that varies from some of the preceding responses and comments.

Point-to-point ticketing may also be Round Trip fares, among others.

An example of Point-To-Point Round Trip ticketing would be:

1st Round Trip Ticket
LAX-ELP (Coupon 1) - Outbound
ELP-LAX (Coupon 2) - Return

2nd Round Trip Ticket
ELP-DAL (Coupon 1) - Outbound
DAL-ELP (Coupon 2) - Return

Flown in the following order:
(Creating a Point-To-Point itinerary)[*]Outbound
LAX-ELP (Coupon 1) - Outbound from 1st Round Trip Ticket)
ELP-DAL (Coupon 1) - Outbound from 2nd Round Trip Ticket)
[*]Return
DAL-ELP (Coupon 2) - Return from 2nd Round Trip Ticket)
ELP-LAX (Coupon 2) - Return from 1st Round Trip Ticket)

By the way, this example would circumvent the Wright Amendment.
Another story for another day.

Tickets are not point-to-point in and of themselves, but become point-to-point when a non-thru segment is combined with at least one other segment, thus creating the point-to-point concept. They may be issued on the same or separate ticket stock or record locator or itinerary. I recall paper tickets that when the entire itinerary was on one set of ticket stock, thru routings were designated differently than point-to-point routings, by either an "X" or an "O" between the line item listing of segments. It's important to weigh the pros and cons when considering point-to-point ticketing. And there are both!

For example, Point-to-Point Vs Thru Routings: [*]Checked Luggage
Point-to-point requires checked luggage to be claimed and rechecked at each point. Thru routings may be checked to your final destination.
[*]Pricing
Pricing requires careful consideration as it can vary greatly. No simple formula here. At times, point-to-point prevails, at other times thru routings.
[*]Segment or Mileage Accrual
This can also vary greatly depending on the airline and the routings.
With Southwest, point-to-point is an advantage in this category. However, it may not be when you factor in other considerations.
[*] Protection With Flight Delays Or Irregularities
This can be a bit tricky. With thru routings, I feel you are much better protected, especially with any flight delays along the way. With point-to-point you are expected to comply with check-in requirements at each respective point. If you are delayed along the way and do not meet the check-in rules, you could be treated differently depending on whether you are booked as a thru or point-to-point passenger.

In the end, it all boils down to a balancing act by taking everything into consideration, determining what works best for you, carefully weighing the pros and cons and doing your homework. And of course, last but not least, perusing FlyerTalk.