The level of difficulty one may face while explaining this to a man who is not from Telecom background depends on his awareness that he already has about current Wireless technologies.
And really you cannot help him much with explanation on this as most of it would be obviously quite technical.
Still one may explain in terms of below mentioned points :-
1) Like data-speed specially in Downlink i.e. in terms of download speed that a common man deals with.In terms of Bandwidth etc.
2) So many always-on applications that people are using on various smartphones. i.e. something related to increasing data usage/traffic etc....
3) Latest high level services being offered to end user like IPTV,live video streaming,true HD & 3D streaming etc..
i.e. focusing on why LTE is required , how such high bandwidth requiring services are feasible etc......
Keep thinking and one may get some points that make sense to a non-technical man.