mrdini, welcome to FT, from another newbie!
Using Krisflyer (SQ's FFP) as an example, even if you do not get to enjoy the benefits during the trip, by the end of your RTW trip, you would have earned enough miles to
- become an Elite Silver member
- redeem an award ticket to as far as Vietnam or Philippines from Singapore
Since your RTW starts and end in LON, I am assuming that you reside in the UK. That means that flying on BMI and Virgin also earn you miles on KF. Star Alliance flights are also eligible for mileage accrual (of course subject to terms and conditions

). Only thing is KF miles only last 3 years before expiring.
Essentially, a FFP is just like Tesco's Clubcard, or Sainsbury's Nectar Card, except that it is largely used in travel.
For more information, visit the various FFP websites:
Singapore Airlines Krisflyer
Virgin Atlantic Flying Club
Air New Zealand Airpoints
Look through the benefits and decide which one is the most suitable for you.
Finally, enjoy your trip!