Gases can be compressed because each gas particle has relatively vast amounts of room between it and all other gas particles the majority of the time. Thus, compression, which is essentially forcing the gas particles closer together, has a great deal of space to reduce. This contrasts with liquids and solids, which have particles in constant contact with one another, and thus little room to compress.
Gas particles are in constant motion, bumping into each other and the walls of any container in random fashion. The frequency and force of these impacts constitutes the pressure of the gas. Outside of a container or some other force, such as gravity, keeping them in place, gas particles actually fly apart entirely. In other words, gases expand to fill any container. When restricted by forces, they exert pressure in opposition to those forces. Compressing a gas increases its pressure. So does heating it, even when volume remains constant.
Regardless of current pressure, compressing a gas is easier than compressing solids or liquids. At a high enough pressure or low enough temperature, gas particles of many substances are forced together so much that some of them form a liquid. This state is relatively easy to achieve with carbon dioxide, for instance.
Gases also expand easily. All gases expand uniformly to fill any container in which they are placed.