The splash term has two meanings in digital marketing context.
The main usage refers to an introduction page displayed before accessing the real home page of a site. In this case, splash pages are often used to let visitors choose an option (e.g., language, country, bandwith, etc.) or to emphasize an offer, event or action sought after (e.g., email sign-up).
Some are created for brand or image purpose, particularly in luxury sector (see an example below).
Splash page can also be used to ask visitors for their age for restricted contents.
Splash page must be associates with cookie implementation to identify returning visitors and bypass the splash page on all subsequent visits to the site.
Splash pages differ slightly from home page overlay. The latter hides only a portion of the homepage.
The use of splash pages is a matter of some debate and condemned for a long time by usability specialists because it can be seen as a disconfort by visitors and be a source of abandons. It can also hurt SEO. Thus, it seems it must be reserved for really special situations or targeted visitor segments.
For instance, it seems to give good results for donation on political website.
In a second meaning splash page may be used to refer to pre-home ad unit. In this case pre-home interstitial seems more appropriate.
An example of splash page on Barack Obama website to optimize donations:
A "personal brand image" purpose:
A splash page for language options which could be easily replaced by automatic redirect based on IP address: