This apple tree has this growth on many of its branches (say, 30%). It also hardly produces any fruit. How can I make this tree healthier?
This kind of growth is typical on a tree that has run out of energy. Instead of making visible new growth each year with nice long shoots at least 10 cm. long it has a hard time putting out a whorl of small leaves on a shoot measuring less than 3 mm. Consequently it does not have the mass of good green foliage to make food to feed the roots, and a cycle of lack of vigour sets in. No roots, no shoots, no roots. The wood hangs on so long in dense clusters that prevent air circulation, and moss starts to grow just as it probably does in the grass under the tree; it is largely cosmetic and will disappear by itself once you get the tree back in good shape.
Review the age of the tree from the trunk size, the amount of competition from other trees in the vicinity, and the quality of the soil it is growing in. You are probably in for a lot of pruning as you open up the tree to allow air circulation and get the annual growth going again with a general purpose fertilizer or well rotted manure. Also review the bark of the tree for signs of damage that prevent the roots from feeding the canopy; examine the base of the tree for vole and mouse damage which can cut off a lot of nutrients. It might take several years of diligent attention to thin out the branches and get the branch ends producing those nice fresh long shoots in spring.