In London, The trains, what do they mean by PEAK and OFF-PEAK?

It's 1.95 per journey. Or about 4 if you travel during peak times. But there's a maximum daily cap (see below). The web site has the full details, but peak is roughly 7am-9.30am and 4.30pm to 7pm. So if you make any journey during those times, it's about £4 rather than 1.95, AND the maximum expenditure for the day is capped at around 8, rather than 4.

Peak times = rush hour periods, when trains are at the busiest. Morning approx 7 - 9.30am and then again afternoon/evening from about 5 - 7pm. The above peak times are approx only. Off peak is the period in between - approx 9.30am to 4.30pm. Off peak times are squeezed by most overhead railway companies in order to collect maximum fares for as many hours of the day as possible. Think we should start a campaign via Parliament to enact a law which states the exact peak and off peak hours. Probably won't happen because the travelling public are like a flock of sheep and just pay up whatever they're asked to pay. Thankfully it no longer bothers me because as a London pensioner I've got the Freedom Pass available to all Londoners from age 60+.

Officially peak travel time is any time BEFORE 9:30 am (i.e. 04:29 am to 9:30 am). There is no evening Peak time for London transport travel. http://www.tfl.gov.uk/tickets/14837.aspx This is what the website says. Travel before 9:30 and you will be charged £1.95.

peak- when the majority of workers are commuting to work in the morning and going home late afternoon/early evening-

I think /mean, it's just easy to find out by yourself!! Peak = is Main-Time; Off Peak = is such kind of "low Season" /time!

All the accurate information you require is on the TFL website you idiot