There are two main obstacles that plants must overcome to grow taller.
The first is just the structural support of the weight of the top of the tree. The second is the transportation of water up to the leaves and sugars down to the roots. Plants solve both problems at the same time by having extremely rigid transport tissues in the trunk -- the xylem (for water) and phloem (for sugary food). Actually it's the xylem that does most of the support work. The cells making up the
long xylem tubes have both cellulose, an extremely tough, but fairly flexible, fibrous polymer, and lignin, a protein that hardens the cell wall and makes it rigid.
The angiosperms (flowering
plants) also have unique cells that make up the xylem called vessel elements -- essentially hollow tubes that lose their nuclei and are more efficient at transporting liquid than the narrower cells called tracheids that make up the xylem in non-angiosperms.
Don't forget, though, that the tallest trees around aren't angiosperms at all -- the redwoods are conifers, so they have cones, not flowers. Redwoods and other conifers don't have a lot of the fancy reproductive adaptations that make angiosperms so specious and successful, and they have tracheids, not vessel elements, in their xylem, but they do have cellulose and lignin and that seems to be enough to let them grow as tall as they do.