The words are baseball metaphors used by Americans when they refer to sexual activities. Perhaps their ides of sex is like a baseball game or perhaps they like baseball so much that they can't resist using these metaphors. Or perhaps they are too inhibited to use the actual terms and resort to these metaphors. Whatever their reasons might be, here are the technical definitions I found from a site -

First Base - commonly understood among Americans as French kissing
Second Base - fondling, groping and stimulation of body outside the clothing
Third Base - heavy petting and fondling of genitals and possibly oral sex
Home Run - The actual having sex alias intercourse.

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American brains in action, in this very forum:
Where else in the world do you find such a mass national delusion of being invaded or bombed?