If no-one has explained (and you might not know) there's 2 levels of editing images: image development and pixel-level editing.
Image development software is what you use for making basic changes to an image, just as though you were developing a photo in the darkroom. You will adjust exposure, contrast, colour balance, sharpness, cropping the picture etc. Examples of this software are DXO optics Pro (free, mentioned above) Lightroom (not free) Dark table and Raw Therapee (both free). They are non-destructive editors that do not change your base image, allowing you to keep you work for re-editing again if needed.
Pixel level editors that you would use for making deep and fundamental changes to your images (like adding or removing things, or changing the nature of the image irreversibly) include Adobe Photoshop, Jasco Paintshop (not free) GIMP and the NIK suite (free).
There's also a class of editor that sits slightly outside these, and will make destructive (i.e. irreversible changes) to your images but can still be used to improve & develop them. Examples are Irfanview (very small, fast and easy to use) and DigiKam (more powerful, still easy but more complex) - both free.