Digitisation usually refers to making collections data, including images and other media, available online. But it may also refer to making any quantitative (e.g. historical datasets) or qualitative information (exhibition and learning resources) available and discoverable via the web.
A digital collection usually comprises an object record describing the object, its composition or makeup and other descriptive elements. It may have an associated image, video, audio or document with it. Sophisticated digital collections will display links to related objects and information. Some are aggregated into larger digital repositories which allow you to search across several collections such as Culture Grid or Europeana.
The digitisation movement in the UK heritage sector started in earnest under the New Opportunities Fund Digitisation (NOF-digi) programme, funded by the National Lottery between 2001-3/4. One of my previous projects, Hantsphere, was part of this. NOF-digi projects taught heritage and cultural technologists a lot about good and bad practice, and most importantly about sustainability. A significant amount of data remains undiscoverable and in some cases has been lost altogether through lack of onward funding and resources within the organisations that ran these projects.