Essentially Clipping multiple times is prolonging the use of the next GCD due to animation lock on the current oGCD skill. This translates into lost casts throughout an encounter. Kabooa's example is pretty much what clipping is, but I'll elaborate what GCD and oGCDs are too.
When you use a skills, sometimes there will be other skills that you haven't used go on cooldown for a brief moment before they are available to be used again. That means those skills are on the GCD.
A GCD is a skill that shares a global cooldown - generally this cooldown is 2.5 seconds before the next skill that shares a global cooldown can be used. This is without spell or skill speed modifiers. GCDs may have their own cooldown in addition to a global cooldown.
Examples of GCDs are:
Cure I, Cure II, Benefic I, Benefic II, Physick, Regen, Aspected Benefic, Adloquium, Stone, Glare, Broil, Dia, Combust, Bio, Malefic, Medica, Medica II, Succor, Aspected Helios, Helios, Afflatus Solace, Afflatus Rapture, Afflatus Misery, Art of War, Raise, Ascend, Resurrection, Shadow Fang
.
An Instant GCD means a skill that is on the global cooldown and can be used instantly, but still requires you to wait the global cooldown before using the next skill with the global cooldown. This is why White Mages cannot cast 3 Afflatus Solace or Afflatus Rapture in 2 seconds even if they have 3 lilies ready and the spell is instant cast. The global cooldown prevents them from doing so, so there is a wait period between casts.
Examples of Instant GCDs are:
Regen, Aspected Benefic, Dia, Combust, Bio, Ruin II, Afflatus Solace, Afflatus Rapture, Afflatus Misery, Art of War
oGCDs are skills that do not share a global cooldown. They can be used without having the 2.5 second wait on all skills that share this timer. These skills have their own cooldown timer associated with them. However, like all skills, they are also subject to an animation lock - so you won't be able to use another skill immediately while you are in animation lock. This animation lock is usually 0.7 seconds. Some are longer - such as Red Mage's Displacement - because you can't also do anything while you are dashing backwards, resulting in a 1.1 second animation lock.
Examples of oGCDs are:
Benediction, Essential Dignity, Lustrate, Indomitability, Celestial Opposition, Tetragammaton, Divine Bension, Assize, Emergency Tactics, Deployment Tactics, Aetherflow, Energy Drain, Lucid Dreaming
While some oGCD skills are weaker that GCD skills, their inherent advantage is that they can be used between GCD skills, thus making them beneficial to use even if they are weak since there would be no downsides to using it. GCD skills are the only skills that have an associated cooldown between multiple skills in addition to their own cooldown in order to be used, so the idea is to use oGCD skills between the GCD skills so you can repeatedly use GCD skills continuously. This is how healers who need to burst heal can keep their GCD rolling while using multiple skills to get the maximum output in a small timeframe without losing casts and how Ninja bursts an enemy down with multiple uses of their oGCD skills per GCD within their Trick attack window.
Example of a GCD with oGCD usage:
Say a box [ XXX(#)--XXX(#)--XXX(#)--(#)] represents a GCD, around 2.5 seconds of time, XXX is a skill, and the (#) in the box represents the duration of that time.
For White Mages:
[ Afflatus Solace (0.7) -- Tetragammaton (1.4) -- Divine Bension(2.1)-- (2.5)] [Glare(0.7)----Glaring(1.4)-------Glare Done(2.5)] ====== total time 5 seconds with 2 GCDs and 4 total skills used in that timeframe.
[Dia(0.7)---Swiftcast(1.4)--Plenary Indulgence(2.1)--(2.5)][Medica II(0.7)---Assize(1.4)--Lucid Dreaming(2.1)--(2.5)] ====== total time 5 seconds with 2 GCDs and 6 total skills used in that timeframe.
[Afflatus Rapture(0.7)--Swiftcast(1.4)--Thin Air(2.1)--(2.5)][Raise(0.7)--Tetragrammaton(1.4)--Assize(2.1)--(2.5)] ====== total time 5 seconds with 2 GCDs and 6 total skills used in that timeframe.
For Astrologians:
[Malefic(0.7)--done(1.5)--Celestial Opposition(2.2)--(2.5)][Malefic(0.7)---done(1.5)--Essential Dignity(2.2)--(2.5)] ==== total time 5 seconds with 2 GCDs and 4 total skills used in that timeframe.
[Malefic(1.5)--Lightspeed(2.2)--(2.5)][Malefic(0.7)--Celestial Intersection(1.4)--Draw(2.1)--(2.5)][Malefic(0.7)--Play(1.4)--Horoscope(2.1)--(2.5)] === total time 7.5 seconds with 3 GCDs and 8 total skills used in that timeframe.
For Scholars:
[Biolysis(0.7)--Aetherflow(1.4)--Chain Strategem(2.1)--(2.5)][Ruin II(0.7)--Sacred Soil(1.4)----(2.1)---(2.5)] === total time 5 seconds with 2 GCDs and 5 total skills used in that timeframe.
[Broil(0.7)---Broiling(1.4)--Broiling Done(2.5)][Ruin II(0.7)--Aetherflow(1.4)--Swiftcast(2.1)--(2.5)][Broil(0.7)--Recitation(1.4)---Excogitation(2.1)--(2.5)] == total time 7.5 seconds with 3 GCDs and 7 total skills used in that timeframe.
Example of a GCD no oGCD usage:
[Medica II(0.7)---casting(1.4)---casting(2.1)-done(2.5)][Afflatus Rapture(0.7)---done(1.4)---(2.1)--(2.5)] ====== total time 5 seconds with 2 GCDs and 2 total skills used in that timeframe.
[Aspected Helios(0.7)---casting(1.4)--done(2)--(2.5)][Benefic I(0.7)---done(1.5)--(2.2)--(2.5)][Benefic II(0.7)---casting(1.4)--done(2)--(2.5)] === total time 7.5 seconds with 3 GCDs and 3 total skills used in that timeframe.
[Succor(0.7)--casting(1.4)---done(2)--(2.5)][Adloquium(0.7)---casting(1.4)--done(2)--(2.5)][Broil(2.5)]=== total time 7.5 seconds with 3 GCDs and 3 total skills used in that timeframe.
Weaving oGCDs between GCDs allow a lot of healing without sacrificing time, eventually letting you cast more of the heavier GCDs that don't allow weaving in that time period, resulting in more potency for both healing and for damaging enemies in the course of the encounter. However, if you start to clip too much to use your oGCD, you essentially lose a GCD skill that you could have fit there in that timeframe. What that means is that you could lose a GCD by using oGCDs, causing oGCD skills to not be free since it costed you a GCD to use it. This eventually bleeds into less healing output and less damage output in the course of the encounter.
Examples of Clipping: Clipped skills in Italics
[Glare (2.5][Dia(0.7)--Assize(1.4)--Lucid Dreaming(2.1)--Plen]ary Indulgence(2.8)[Medica II(2.5)] ==== total time 7.8 seconds with 3 GCDs and 6 total skills used in that timeframe.
[Broil(2.5)][Adloquium(2)--Emer]gency Tactics(2.7)[Adloquium(2)--Reci]tation(2.7)[Adloquium(2)--Deplo]yment Tactics(2.7) === total time 10.6 seconds with 4 GCDs and 6 total skills used in that timeframe.
[Malefic(1.5)--Draw(2.2)--P]lay(2.9) [Aspected Helios(2)--Celestial] Opposition(2.7)[Malefic(2.5)] ===== total time 5.6 seconds with 2 GCDS and 5 skills used in that timeframe.
[Malefic(1.5)--Draw(2.2)--P]lay(2.9)--Neutral Sect(3.6)[Aspected Helios(2)--Essential] Dignity(2.7) === total time 6.3 seconds with 2 GCDs and 6 skills used in that timeframe.
Although the effect of clips may seem small, such as 0.6 seconds of clipping maybe every 30 seconds, if an encounter takes 10 minutes, and the healer is continuously clipping every 30 seconds for 0.6 seconds, that results into 12 seconds of clipping. 12 seconds could be almost 5 GCDs, which could mean 5 missed aspected helios, 5 missed Succors, 5 missed Cure II, or 5 missed glares. That's a lot of healing output and damage output lost overtime to simply clipping. Generally, it could be more depending on if the boss has phase transition mechanics or untargetable moments, causing each clip to prevent the last GCD from happening.