Why does the person reading the personal statement have to understand what leading is? What message are you trying to get across by saying you've lead the pitch?
My guess is that you want them to understand the qualities and transferrable skills that leading a pitch shows you have. If this is the case, perhaps emphasise these qualities instead of discussing the concept of leading? If you then get to chat in person you could explain where this experience comes from.
- You are responsible for the very-real safety of the team.
- You make dynamic risk assessments in a time-pressured setting.
- You select appropriate techniques and equipment for a given situation where you may have incomplete information.
- You are trying to continually gather information to help you make the best decisions.
The downside of this approach could be that to the lay-person it may conjure the image of a Himalayan expedition with a large team instead of, potentially, a single-pitch of climbing.
In more general terms, I usually describe leading in the following way to non-climbers when I'm having a conversation with them. This is wordy so probably not suitable for your needs:
Leading a pitch is climbing up a section of rock face with the rope below you instead of coming down from above. As you climb you are responsible for attaching the rope to the rock when you can. If you fall then you will free-fall at least twice the distance to your last attachment point before the rope starts holding you, for example if it's last attached half a metre below you then you will free-fall at least one metre. This is in contrast to when you are seconding or top roping a climb where the rope will hold you where you are the moment you fall.
To combine these ideas you could try something like:
The climber leading a pitch is the first person in the team to go up a section of rockface, taking responsibility for the safety of the entire team.
Because the rope is attached below the leader the consequences of falling are greater than the person climbing behind you, who will have the rope above them. The leader has to use their skill, experience and equipment to conduct and implement dynamic risk assessments on unknown ground.
You may find the first sentence is sufficient if you are short of space.
As an aside, I don't like referring to crags as a rockface, but in my experience, this term conjures the closest image to what we mean in the minds of non-climbers.