It only means that the plants have been in place long enough to reach, or at least approach, maturity; they are not little sticks, they are full-sized shrubs, perennials, and trees. What it means to you and your gardeners is that they are much more likely to survive bad weather, neglect, and injury.

You might not have to fertilize, if the plants are happy, but I do recommend that you mulch your garden, as it will help to keep the soil moist and to keep the weeds to a minimum.

If I was coming to tend your garden I would be largely looking at a routine of feeding, mulching, and pruning for appearance. I would be striving against shade to keep any groundcover other than moss or bare in patches near some of the shadier trees.

I would find it quite difficult to grow any fresh perennials or bulbs that need lifting for refreshment. I'd possibly look at 'bombproof' plants such as Hemerocallis 'Stella d'Oro' to give me a burst of summer colour.

The biggest problem I would have would be the network of roots which will be under the lawn, paths, and even the house.

I'd hope that your maintenance person has the gear for cleaning the gutters in autumn/fall...

You may need to add your colour and contrasts through using pots and other garden decoration because of root competition. Big enough pots to be part of the architecture and not a dismal view of a desperate gardener ;-) with dozens of spotty little pots. Matching or linked by shape, material, colours. And kid-safe.

If you want to grow herbs or veggies for your kitchen, I'd hope you have a sunny spot. You can make or buy raised beds, at need, but anything with an open bottom will soon attract wandering roots. From surprising distances.

The plus for you is - fairly low work levels - apart from weekly grooming in season, and pleasant shelter in summer so the kids can play without sunburn risk.

Don't know your area - be meticulous about avoiding standing water in pots or similar. You may find your delightfully shady yard is also a haven for mosquitoes.

Hope that helps.