Also make sure that your gamemode is not set to adventure mode.
for regular survival mode enter :
for creative mode enter :
for adventure mode enter:
Survival mode is just the Minecraft as everybody knows it and this is probably the mode you want to be changing to.
Creative is the mode in which you have unlimited blocks and resources to build everything in your imagination. You also have the ability to fly.
Adventure mode is the same as survival only you don't have the ability to destroy any blocks without the correct tool.
If you are playing on a multiplayer server you might be building or changing to close to spawn. Try walking in one direction for a few seconds and try it again then.
Also clicking does not break (many) blocks, you need to click and hold. Initially only a few block types can be feasibly broken using only your hand, including dirt/grass, sand, wood and leaves, so try left-clicking and holding and see if you can break these types of blocks.
Finally, check if you have "touchscreen mode" enabled under control settings. This can often mess with block breaking.