I can only speak to FSX, though I'm sure X-Plane is technically very similar...
1)
Mesh is the 3-D shape of the terrain, particularly the mountains vs. valleys. Elevation data points are connected to create the topography. The closer the points of data are to each other, the more accurate the topography is.
Depending on what region of the world you are improving, mesh either gives dramatic results or very little 'bang for the buck.' FSX generally renders North America fairly well, but other regions--especially mountainous areas--can benefit greatly by adding good, high resolution meshes. Mesh is usually cheap, easy to install, and a good starting point for beginners. FSGenesis is an example of developer that specializes in mesh replacements. Some landclass products (see below) also include their own replacement mesh, so be careful of that.
2)
Terrain textures are image samples of different kinds of topographical features (forests, fields, farms, parking lots, rocks, sand, apartments, shopping centers, swimming pools, etc.) that are distributed crazy-quilt style over the mesh. They aren't specific to a particular place; they are general and can represent any urban, suburban or rural area on the continent during every season that region would experience. Ground Environment X is an example of a payware terrain textures replacement product.
3)
Landclass is the data that places all of the terrain textures, plus carves the coastlines and water bodies, places roads and railroads, and places the generic 3-D "autogen" features like trees, houses, factories, windmills, moving cars and trucks, etc. Ultimate Terrain X is an example of a landclass product, albeit a very feature-rich one, and it is designed to work hand-in-hand with Ground Environment X textures. Scenery TECH is another landclass developer.
4)
Photoscenery is a different approach to 'painting' the mesh than the default Landclass method, and it replaces generic textures with a large aerial photo of a specific region. It's essentially like using Google Earth. The advantage of Photoscenery is that you can sight-see actual terrain features like your own house. The disadvantages are that photoscenery usually only represents one season; it looks pixelated at low altitudes; and using it eliminates autogen features like 3-D trees and buildings. The MegaScenery Earth series and the VFR Real Scenery series are examples of photoscenery products. (Some of the major airports in FSX use photoscenery as their base.)
5) Clouds and weather visuals can be improved with products like Real Environment Xtreme. You can download very high resolution REX textures if you choose, although these do take up a huge amount of hard drive space and will slow overall performance.
6) Specific sceneries like airports usually are prioritized to sit above the mesh, landclass and photoscenery.
As you can see, there are many options towards customizing FSX.
For simplicity's sake, I recommend that you consider starting with a combination of
Real Environment Xtreme and
ORBX Full Terrain products. The FTX modules are easy to install and use as a progressive build, and the scenery looks great.