A relaxed performance is a specially adapted show, modified for adults and children who might benefit from a more relaxed environment. Typically, they are for people who have autism or have sensory communication disorders or learning difficulties and some theatres also occasionally run them for people with dementia. A standard performance of a show can be unsettling for people with the above conditions. This could be because of the darkness of the auditorium, the loud music and sudden noises on stage, not to mention the expectation that a child must sit still and quiet for a relatively long period of time.
Relaxed performances differ from theatre to theatre, so you should always check with each venue first. But generally, at a relaxed performance it is a more informal atmosphere; the house lights don't go down as much as they normally would and in some cases are kept on entirely. Strobe lighting is avoided and if there is music then it tends to be played more quietly with no loud or sudden sound effects.
Often venues will also provide a "chill-out" zone for you to take your children to if they become distressed and quite often the theatre staff and the cast will have been briefed on how to help children with special needs.
Perhaps most importantly there is an acceptance that if your children chatter, shout out, make noises or fidget, it's absolutely fine! Tutting is most definitely not tolerated so that you can also relax without worrying that his behaviour is disrupting other patrons.
So many amazing and reputable theatre venues and companies now schedule in a relaxed performance of their productions just as they would a signed or audio-described performance, so always check with the box office to see if such an option is available. If your local venue doesn't offer relaxed performances why not write to the artistic director or general manager asking them to consider doing one in the future?